PhxDraw - CINVESTAVdelta.cs.cinvestav.mx/~mcintosh/cellularautomata/Papers... · 2011. 10. 4. · p8x.draw February 14, 1994 width 4 width 5 width 6 width 7 width 8 width 9 width

PhxDrawA Portfolio of Phoenix

and

Their de Bruijn Diagrams

Harold V. McIntosh

March 11, 1994

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Phoenix de Bruijn diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 WIDTH 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

width 4 - s.dat connection list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 WIDTH 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13


6 WIDTH 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

width 6 - s.dat linkage list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7 WIDTH 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20


8 WIDTH 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32


width 8 - z.dat Zero component connections . . . . . . . . . . . . . . . . . . . . . 58

9 WIDTH 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

width 9 - s.dat full linkage list . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

width 9 - z.dat zero linkage list . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

10 WIDTH 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

width 10 - z.dat linkage list of zero component . . . . . . . . . . . . . . . . . . . 125

11 WIDTH 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

width 11 - z.dat zero component connection list . . . . . . . . . . . . . . . . . . . 144

12 WIDTH 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

List of Figures

1 self link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 alpha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 gamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6 small . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

7 zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1 Introduction

p8x.draw February 14, 1994

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A Phoenix is a Life configuration in which each

and every member of a given generation disappears;

nevertheless while that is happening they succeed in

bringing forth a new generation, so preserving the

population indefinitely.

Here each phoenix has period 2, and is confined to

a strip, whose de Bruijn diagram was calculated

for the widths listed in the following index:

1

2 Phoenix de Bruijn diagrams

This current de Bruijn analysis began some time ago when someone asked about that huge blinkerwhich appeared on the front cover of Scientific American along with one of Martin Gardner’scolumns about Life. The immediate reaction was that they were something of a triviality, giventhat the two tiles (shall we call them a and b?)

1 . 1 .2 2 2 21 1 and 1 12 . . 2

could be strung out into chains, and could easily turn corners. Such a configuration is calleda phoenix, for the obvious reason that each generation disappears completely as it generates itssuccessor. There are some other things which fulfill the requirement; many of them connect tofigures which remain constant from generation to generation. The barber pole is an example of oneof them.

The phoenix condition is restrictive enough that the de Bruijn diagrams for some narrow stripsand low periods could be calculated on a PC. When Gerardo Cisneros worked out the spaceships,he also extended the phoenix results, but their analysis was left until after the examination ofthe spaceships. Now it is their turn; here are some results for freestanding figures. Quiescence atinfinity in one direction is imposed from the outset, but in the orthogonal direction it depends onwhether the zero tile is an isolated component or not.

width ofnonzero number of number of consolidatedcolumn nodes links nodes components

--------- --------- --------- ------------ -----------1,2,3 1 1 1 1

4 17 17 3 35 33 33 5 56 71 79 14 67 145 171 55 48 337 411 137 109 818 970 .. 4410 1845 2187 .. 9811 4556 5640 .. 9112 11229 14607 .. 50

Having analyzed the spaceship diagrams in considerable detail, it is interesting to look at thesimilarities and differences between the two systems.

In both cases, the minimum width is 4, but one of the first points for conjecture concerns itsvalue in general. Unless the diagram is forbidden - for example, by the first level having no linksto zero, or there exists an independent proof that the figures do not exist - such a width is to beexpected. That it is not too small is reasonable, and there is a (generally) extravagant upper limit(the maximum cycle length in the first level diagram).

For spaceships, the smallest figure had three components; that zero was one of them implied thatthere was no configuration of finite vertical extent. The same is true here; as with the spaceship,

2

each generation belongs to its own component. Unlike the spaceship, for which each component issymmetric by vertical reflection, the two generations, strings of a tiles and their vertical reflections,are mutual reflections, as is evident from examining the tiles displayed above.

At width 5, the only variation possible is the centering of the filaments of width 5, since theycannot be bridged.

Two possibilities arise at width 6 — the b tile can be used to shift the filament over by TWO cells,and two new tiles can be used to line up a tiles against the outer walls of the strip. There are threecenterings for the a- and a’- filaments, but the center one admits of no variation. Consequently thereare six components: zero is still isolated, alpha and beta respectively hold the filaments hugging thewalls and crossing over, two for the generations of the central filament, and a gamma component.

At width 7 there are only four components - zero (1 consolidated node), alpha and beta, (with14 consolidated nodes each) and gamma (with 26 consolidated nodes).

Width 8 is the significant width, of course, because it is the smallest width for which thezero tile is no longer isolated; this is a consequence of the formation of a ring of four a-tiles, butunfortunately there is still not enough wriggle room for attaching anything else to the ring - forexample, to extend its vertical edges. Such rings do have a compressed version, already visible atwidth 7, which fits sideways into the strips, since it can be stabilized by connecting it to filaments,which can eventually terminate on a mirror image or something else suitable. But nothing in theassemblage is yet sufficient to make it freestanding.

However, it requires width 10 to get a zero-component with any appreciable versatility.

Width 8 also accomodates parallel avatar filaments, if they are packed just right; there are threepackings of two generations each, for a total of 6 isolated components; together with zero, alpha,beta, and gamma (which are enlargements of their respective themes) making a total of 10.

Giving the possibility of twisting and turning, notably of the a-tiles abetted by the b-tiles, thephoenix avatar structure is not so pronounced as for the spaceships. Nevertheless it is readily visibleand exerts a strong influence on the structure of the diagrams and the physical appearance of aphoenix.

At widths of eight and greater, the packing of multiple filaments, and the arbitrariness oftheir placement with respect to one another generates a myriad of components. In particular,filaments 4 wide can be stacked in 3 different ways without interference. Thus width 8 has 6isolated components, 3 each for the two generations, which are pure cycles of the 8 joined pairs ofa-tiles and their reflection. For width 14, there will be 18, 9 each for the generations is which threefilements stretch alongside each other, and so on.

Slightly wider strips allow more relative displacements, up to all 8 possible shifts; but at thesame time shifting and joining become possible, resulting that the components no longer consist ofa single cycle, and thus become less and less isolated.

Doubtless the same phenomenon occurs for spaceships, but for them it was only beginning tomanifest itself at the widest strips which it was possible to examine.

3

In reading the de Bruijn diagram, note that a node with a single isolated incoming arrow isself-linked.

0 self-link

Figure 1: self link

4

3 Components

Alpha component

width comments

4 two avatars, alpha and beta, in 4x8 unit cell

5 two positionings of the avatar give separate components

6 centered alpha in one component, with transitions from

full left to full right included in a second component.

7 four positionings short loops in a single component.

8 five positions and short loops in a single component.

9 six positions, short loops, horizontal bridge tiles, and

the accomodation of two parallel alpha filaments. all

within a single component.

10 seven positions

11 eight positions

12 nine positions

December 4, 1996alpha.draw

1

1

Figure 2: alpha

5

Beta component

width comments

4 two avatars, alpha and beta, in 4x8 unit cell

5

6

7 The beta component is the alternate generation

8 of the alpha component, differring from it by

9 mirror reflection perpendicular to the glide axis.

10 seven positions

11 eight positions

12 nine positions

December 4, 1996beta.draw

2

2

Figure 3: beta

6

Isolated cycles

width comments

0-3 the only "phoenix" is the quiescent zero, a 1-cycle

4 zero and the alpha and beta avatars are all cycles

5 zero and two positionings of two avatars are all cycles

6 zero, and centered alpha and beta filaments are cycles

7 zero is the only cycle

8 there are six cyclic strand pairs, 3 alpha and 3 beta

9 38 cycles formed by pairing alpha and/or beta strands

10 71 cycles of various compositions including strands and

cross-linked strands, generally having alpha or beta

borders.

December 4, 1996cycle.draw

2

2

Figure 4: cycles

7

Gamma component

width comments

6 single aligned alpha-beta pair with cross links (avatar)

7 single gamma strand can shift at nodes

8 single gamma strand can shift at nodes or loops

9 single gamma strand has more shifting flexibility

10

11

12

December 4, 1996gamma.draw

58

44

56

67

58

56

66

41

58

Figure 5: gamma

8

Small components

width comments

0-8 there are no narrow "small" (neither cycles nor named)

9 6-node cross linked alpha pair, another with beta edges

10 18 with 3 (8), 4 (2), 6 (4), 7 (4) nodes

December 4, 1996small.draw

2

2

Figure 6: small

Zero component

width comments

1 ... 7 trivial

8 2 rings representing 2 phases

9 2 phases, 2positions, close packing links

10 2 phases, 3 positions, packing, extended rings

11 2 phases, 4 positions, packing, extended rings

12 2 phases, 5 positions, extensive looping

December 4, 1996zero.draw

178

91

Figure 7: zero

9

4 WIDTH 4

Width 4

pg4 - de Bruijn diagrams

s.dat - connection list

17 nodes

17 links

3 components

(all cycles)

maximum linkage: 1

consolidated nodes: 3

consolidated links: 3

component nodes links

zero 1 1

alpha 1 1

beta 1 1

10

Life phoenix de Bruijn diagram, width 4

November 21, 1996pg4.draw

0 0

2

1

1

2

zero component

alpha component

beta component

1

1

2

2

3 tiles

11

Width 4 - s.dat Connection list

- 0000 .... 0 ( 0) 0= 0000 .... 0 ( 0) 0

--- new component ---

prospective tiles: 1- 0051 ..oo 15 ( 1) 3- 00a2 .... 1 ( 3) 5- 0144 .o.. 3 ( 5) 6- 0288 .... 5 ( 6) 10- 1500 oo.. 6 ( 10) 12- 2a00 .... 10 ( 12) 13- 4410 ..o. 12 ( 13) 15- 8820 .... 13 ( 15) 1= 0051 ..oo 15 ( 1) 3


prospective tiles: 2- 0054 ..o. 8 ( 2) 4- 00a8 .... 2 ( 4) 9- 1140 oo.. 4 ( 9) 11- 2280 .... 9 ( 11) 14- 4500 .o.. 11 ( 14) 16- 8a00 .... 14 ( 16) 7- 0411 ..oo 16 ( 7) 8- 0822 .... 7 ( 8) 2= 0054 ..o. 8 ( 2) 4


prospective tiles: 3

12

5 WIDTH 5

Width 5

pg5 - de Bruijn diagrams


33 nodes

33 links

5 components

(all cycles)

maximum linkage: 1




zero 1 1

alpha 1 1

alpha 1 1

beta 1 1

beta 1 1

13


November 21, 1996pg5.draw

5 tiles

0

1

2

zero component

alpha component

beta component

1

2

8

9

8

9

0

2

2

1

1

8

8

9

9

14


- 00000 ..... 0 ( 0) 0


- 00051 ...oo 23 ( 1) 3- 000a2 ..... 1 ( 3) 5- 00144 ..o.. 3 ( 5) 6- 00288 ..... 5 ( 6) 15- 01500 .oo.. 6 ( 15) 18- 02a00 ..... 15 ( 18) 20- 04410 ...o. 18 ( 20) 23- 08820 ..... 20 ( 23) 1


- 00054 ...o. 10 ( 2) 4- 000a8 ..... 2 ( 4) 13- 01140 .oo.. 4 ( 13) 16- 02280 ..... 13 ( 16) 21- 04500 ..o.. 16 ( 21) 24- 08a00 ..... 21 ( 24) 7- 00411 ...oo 24 ( 7) 10- 00822 ..... 7 ( 10) 2


- 00510 ..oo. 31 ( 8) 11- 00a20 ..... 8 ( 11) 14- 01440 .o... 11 ( 14) 17- 02880 ..... 14 ( 17) 26- 15000 oo... 17 ( 26) 28- 2a000 ..... 26 ( 28) 29- 44100 ..o.. 28 ( 29) 31- 88200 ..... 29 ( 31) 8


- 00540 ..o.. 22 ( 9) 12- 00a80 ..... 9 ( 12) 25- 11400 oo... 12 ( 25) 27- 22800 ..... 25 ( 27) 30- 45000 .o... 27 ( 30) 32- 8a000 ..... 30 ( 32) 19- 04110 ..oo. 32 ( 19) 22- 08220 ..... 19 ( 22) 9

15

6 WIDTH 6

Width 6

pg6 - tiles and de Bruijn diagram

s.dat - linkage list

71 nodes

79 links

6 components

maximum linkage: 3




zero 1 1

alpha 1 1

alpha 2 2

beta 1 1

beta 2 2

gamma 8 12

16

68

67

39

41

66

5658

44

68

67

39

41

44

66

56

58

gamma


February 20, 1994pg6.draw

0

0

zero

15 tiles

21

23

21

23

beta

9

9

20

32

20

alpha

32

8

8

20

32

20

alpha at leftor right

58

44

56

67

58

56

66

41

58

gamma,showingall threelinkagestyles

39

56

68

58

alpha incenter

8

8

17

Width 6 - s.dat linkage list

- 000000 ...... .......... 0 ( 0) 0..........

--- new component ---- * 004410 ....o. ..... 18 28 ( 20) 26..........- 008820 ...... .......... 20 ( 26) 1..........= 000051 ....oo .......... 26 ( 1) 3..........+ 0000a2 ...... .......... 1 ( 3) 5..........+ 000144 ...o.. .......... 3 ( 5) 6..........+ 000288 ...... .......... 5 ( 6) 15..........+ 001500 ..oo.. .......... 6 ( 15) 18..........+ 002a00 * ...... .......... 15 ( 18) 20 32.....

- * 014400 .o.... ..... 18 28 ( 32) 37..........- 028800 ...... .......... 32 ( 37) 55..........- 150000 oo.... .......... 37 ( 55) 59..........- 2a0000 ...... .......... 55 ( 59) 61..........- 441000 ..o... .......... 59 ( 61) 65..........- 882000 ...... .......... 61 ( 65) 22..........= 005100 ..oo.. .......... 65 ( 22) 28..........+ 00a200 * ...... .......... 22 ( 28) 20 32.....

--- new component ---- * 004500 ...o.. ..... 16 45 ( 21) 27..........- 008a00 ...... .......... 21 ( 27) 7..........- 000411 ....oo .......... 27 ( 7) 10..........- 000822 ...... .......... 7 ( 10) 2..........= 000054 ....o. .......... 10 ( 2) 4..........+ 0000a8 ...... .......... 2 ( 4) 13..........+ 001140 ..oo.. .......... 4 ( 13) 16..........+ 002280 * ...... .......... 13 ( 16) 21 23.....

= * 005400 ..o... ..... 16 45 ( 23) 29..........+ 00a800 ...... .......... 23 ( 29) 51..........+ 114000 oo.... .......... 29 ( 51) 57..........+ 228000 ...... .......... 51 ( 57) 63..........+ 450000 .o.... .......... 57 ( 63) 69..........+ 8a0000 ...... .......... 63 ( 69) 40..........+ 041100 ..oo.. .......... 69 ( 40) 45..........+ 082200 * ...... .......... 40 ( 45) 21 23.....

--- new component ---- 000510 ...oo. .......... 47 ( 8) 11..........- 000a20 ...... .......... 8 ( 11) 14..........- 001440 ..o... .......... 11 ( 14) 17..........- 002880 ...... .......... 14 ( 17) 33..........- 015000 .oo... .......... 17 ( 33) 38..........- 02a000 ...... .......... 33 ( 38) 42..........- 044100 ...o.. .......... 38 ( 42) 47..........- 088200 ...... .......... 42 ( 47) 8..........

18

--- new component ---- 000540 ...o.. .......... 25 ( 9) 12..........- 000a80 ...... .......... 9 ( 12) 30..........- 011400 .oo... .......... 12 ( 30) 35..........- 022800 ...... .......... 30 ( 35) 43..........- 045000 ..o... .......... 35 ( 43) 48..........- 08a000 ...... .......... 43 ( 48) 19..........- 004110 ...oo. .......... 48 ( 19) 25..........- 008220 ...... .......... 19 ( 25) 9..........

--- new component ---- 883040 ..o... .......... 62 ( 68) 24..........= 006090 ....o. .......... 68 ( 24) 54..........+ 11c020 oo.... .......... 24 ( 54) 58..........

- 882140 ...o.. .......... 62 ( 67) 31..........= 014280 .o.... .......... 67 ( 31) 36..........+ 028411 ....oo .......... 31 ( 36) 56..........

- 040388 ...o.. .......... 70 ( 39) 49..........- 090600 .o.... .......... 39 ( 49) 34..........= 020c11 ....oo .......... 49 ( 34) 56..........

= 041288 ..o... .......... 70 ( 41) 46..........+ 082410 ....o. .......... 41 ( 46) 53..........+ 114820 oo.... .......... 46 ( 53) 58..........

= 050288 .o.... .......... 70 ( 44) 50..........+ 0a0411 ....oo .......... 44 ( 50) 56..........

- 882050 ....o. .......... 62 ( 66) 52..........= 1140a0 oo.... .......... 66 ( 52) 58..........

- 2 150822 oo.... 34 36 50 ( 56) 60..........= 2a0054 ....o. .......... 56 ( 60) 62..........+ 4410a8 2 ..o... .......... 60 ( 62) 66 67 68

- 2 228051 ....oo 52 53 54 ( 58) 64..........= 4500a2 .o.... .......... 58 ( 64) 70..........+ 8a0144 2 ...o.. .......... 64 ( 70) 39 41 44

19

7 WIDTH 7

Width 7

pi7 - alpha component

pii7 - alpha examples

pj7 - beta component

pjj7 - beta diagram

pk7 - gamma component

pkk7 - gamma examples


maximum linkage: 3




zero: 1 1

alpha: 13 20

beta: 13 20

gamma: 26 37

145 nodes

171 links

4 components

20


February 15, 1994pi7.draw

alpha component13 nodes20 links

22

6

49

37

98

34

134

138

75

109

124

22

3

6

34

49

75

37

98

124

134

138

125

109

3

(self)

(self)

125

21


February 17, 1994pii7.draw

alpha component

14 nodes

124

109

125128138

124

109

125128138

37

22

3

34

124

109

125128134

49

75

125128138

124

98

3

6

37

34

124

98

3

34

124

98

3

22


February 15, 1994pj7.draw

beta component

13 tiles20 links

10

4

50

13

25

23

135

54

139

142

141

79

10

79

141

23

142139

122

54

135

4

13

(self)

(self)

25

50

The beta componentis the phase alternate

of the alpha component.

122

23


November 18, 1996pjj7.draw

beta component

13 tiles20 links

23

10

13 135

79

139 142

54 141

(self)50

(self)

25

122

4

24


February 15, 1994pk7.draw

gamma component

26

73

103

45

48

51

136

52

64

140

65

112

68

80

102

77

89

91

82

96

97

107

121

123

123

96

121

140

123

96

121

140

26 tiles

104 26 68

73

82

45

48

51 77

64 65

80

121

136

137

140

52112

123

89

91

96

97107

102

103

104

137

25


February 15, 1994pkk7.draw

gamma component123

89 97 73 82

51 65112123

89 97 73 82

51 65112

45

77

104 26 73 82

45

77

104 26 73 82

91

123

91

123

77

103

77

103

121

137

121

137

82

48

82

48

121

140

123

96

121

140

123

96

121

136112123

96

121

136112123

96

26


- 0000000 ....... .......... 0 ( 0) 0..........



- * 0004410 .....o. ..... 19 31 ( 22) 29..........- 0008820 ....... .......... 22 ( 29) 1..........= 0000051 .....oo .......... 29 ( 1) 3..........

- * 00000a2 ....... ..... 1 27 ( 3) 5..........= 0000144 * ....o.. .......... 3 ( 5) 6 34.....

= 0000288 ....... .......... 5 ( 6) 16..........+ 0001500 ...oo.. .......... 6 ( 16) 19..........+ 0002a00 * ....... .......... 16 ( 19) 22 37.....

- * 0044100 ....o.. ..... 44 66 ( 49) 61..........- 0088200 ....... .......... 49 ( 61) 8..........= 0000510 ....oo. .......... 61 ( 8) 11..........+ 0000a20 ....... .......... 8 ( 11) 15..........+ 0001440 ...o... .......... 11 ( 15) 18..........+ 0002880 ....... .......... 15 ( 18) 38..........+ 0015000 ..oo... .......... 18 ( 38) 44..........+ 002a000 * ....... .......... 38 ( 44) 49 75.....

- * 0014400 ..o.... ..... 19 31 ( 37) 43..........- 0028800 ....... .......... 37 ( 43) 76..........- 0150000 .oo.... .......... 43 ( 76) 85..........- 02a0000 ....... .......... 76 ( 85) 92..........- 0441000 ...o... .......... 85 ( 92) 101..........- 0882000 ....... .......... 92 ( 101) 24..........= 0005100 ...oo.. .......... 101 ( 24) 31..........+ 000a200 * ....... .......... 24 ( 31) 22 37.....

- 0806090 .....o. .......... 88 ( 98) 33..........- 000c020 ....... .......... 98 ( 33) 27..........= 0008051 .....oo .......... 33 ( 27) 3..........

= 0010388 ..o.o.. .......... 5 ( 34) 39..........+ 0020600 ....... .......... 34 ( 39) 113..........+ 1140c11 oo...oo .......... 39 ( 113) 124..........

+ * 2a00000 ....... ..... 118 119 ( 125) 128..........- 4410000 * ..o.... .......... 125 ( 128) 134 138.....

- 8820000 ....... .......... 128 ( 134) 53..........= 0051000 ..oo... .......... 134 ( 53) 66..........+ 00a2000 * ....... .......... 53 ( 66) 49 75.....

27

- 8830100 ..o.o.. .......... 128 ( 138) 55..........= 0060200 ....... .......... 138 ( 55) 116..........+ 11c0411 oo...oo .......... 55 ( 116) 124..........

= * 0144000 .o..... ..... 44 66 ( 75) 84..........+ 0288000 ....... .......... 75 ( 84) 118..........+ 1500000 oo..... .......... 84 ( 118) 125..........

- 0906080 .o..... .......... 88 ( 109) 78..........= 020c000 ....... .......... 109 ( 78) 119..........+ 1508000 oo..... .......... 78 ( 119) 125..........

- * 2280822 ....... ..... 113 116 ( 124) 132..........= 4500054 .o...o. .......... 124 ( 132) 143..........+ 8a010a8 ...o... .......... 132 ( 143) 88..........+ 0403040 * ...o... .......... 143 ( 88) 98 109.....



- * 0000822 ....... ..... 7 58 ( 10) 2..........= 0000054 * .....o. .......... 10 ( 2) 4 13.....

= 00000a8 ....... .......... 2 ( 4) 14..........+ 0001140 ...oo.. .......... 4 ( 14) 17..........+ 0002280 * ....... .......... 14 ( 17) 23 25.....

- * 0004500 ....o.. ..... 17 59 ( 23) 30..........- 0008a00 ....... .......... 23 ( 30) 7..........= 0000411 .....oo .......... 30 ( 7) 10..........

- * 0045000 ...o... ..... 41 99 ( 50) 62..........- 008a000 ....... .......... 50 ( 62) 21..........- 0004110 ....oo. .......... 62 ( 21) 28..........- 0008220 ....... .......... 21 ( 28) 9..........= 0000540 ....o.. .......... 28 ( 9) 12..........+ 0000a80 ....... .......... 9 ( 12) 35..........+ 0011400 ..oo... .......... 12 ( 35) 41..........+ 0022800 * ....... .......... 35 ( 41) 50 54.....

= 00010a8 ...o... .......... 2 ( 13) 20..........+ 0003040 ...o... .......... 13 ( 20) 69..........+ 0106090 .o...o. .......... 20 ( 69) 79..........

= * 0005400 ...o... ..... 17 59 ( 25) 32..........+ 000a800 ....... .......... 25 ( 32) 70..........+ 0114000 .oo.... .......... 32 ( 70) 81..........+ 0228000 ....... .......... 70 ( 81) 94..........+ 0450000 ..o.... .......... 81 ( 94) 105..........

28

+ 08a0000 ....... .......... 94 ( 105) 47..........+ 0041100 ...oo.. .......... 105 ( 47) 59..........+ 0082200 * ....... .......... 47 ( 59) 23 25.....

- 8820388 ....o.. .......... 129 ( 135) 46..........= 0040600 ....... .......... 135 ( 46) 58..........+ 0080c11 .....oo .......... 46 ( 58) 10..........

= * 0054000 ..o.... ..... 41 99 ( 54) 67..........+ 00a8000 ....... .......... 54 ( 67) 111..........+ 1140000 oo..... .......... 67 ( 111) 122..........

- 8830288 ..o.... .......... 129 ( 139) 56..........= 0060400 ....... .......... 139 ( 56) 117..........+ 11c0800 oo..... .......... 56 ( 117) 122..........

+ * 2280000 ....... ..... 111 117 ( 122) 131..........- 4500000 * .o..... .......... 122 ( 131) 141 142.....

- 8a01000 ...o... .......... 131 ( 142) 87..........= 0403000 ...o... .......... 142 ( 87) 108..........+ 0906010 .o...o. .......... 87 ( 108) 79..........

- 8a00000 ....... .......... 131 ( 141) 90..........= 0411000 ..oo... .......... 141 ( 90) 99..........+ 0822000 * ....... .......... 90 ( 99) 50 54.....

- * 020c020 ....... ..... 69 108 ( 79) 120..........= 1508051 oo...oo .......... 79 ( 120) 126..........+ 2a000a2 ....... .......... 120 ( 126) 129..........+ 4410144 * ..o.o.. .......... 126 ( 129) 135 139.....



- 0883040 * ...o... .......... 93 ( 104) 26 68.....

= 0006090 .....o. .......... 104 ( 26) 73..........

+ * 011c020 .oo.... ..... 26 97 ( 73) 82..........

- 0882140 ....o.. .......... 93 ( 103) 36..........= 0014280 ..o.... .......... 103 ( 36) 42..........+ 0028411 .....oo .......... 36 ( 42) 77..........

- 0040388 ....o.. .......... 106 ( 45) 63..........- 0090600 ..o.... .......... 45 ( 63) 40..........= 0020c11 .....oo .......... 63 ( 40) 77..........

= 0041288 ...o... .......... 106 ( 48) 60..........

29

+ 0082410 .....o. .......... 48 ( 60) 72..........+ 0114820 .oo.... .......... 60 ( 72) 82..........

= 0050288 * ..o.... .......... 106 ( 51) 64 65.....

- 8820500 * ....o.. .......... 130 ( 136) 52 112.....

= 0050a00 ..o.... .......... 136 ( 52) 64..........

+ * 00a0411 .....oo ..... 51 52 ( 64) 77..........

- 8830400 ..o.... .......... 130 ( 140) 57..........= 0060900 ....o.. .......... 140 ( 57) 115..........+ 11c0200 oo..... .......... 57 ( 115) 123..........

= 00a0500 ....o.. .......... 51 ( 65) 112..........

+ * 1140a00 oo..... ..... 65 136 ( 112) 123..........

= 0106080 .o..... .......... 104 ( 68) 80..........

+ * 020c110 ....oo. ..... 68 107 ( 80) 121..........

- 0882050 .....o. .......... 93 ( 102) 71..........= 01140a0 .oo.... .......... 102 ( 71) 82..........

- 8821400 ...o... .......... 130 ( 137) 74..........= 0142800 .o..... .......... 137 ( 74) 83..........+ 0284110 ....oo. .......... 74 ( 83) 121..........

- 2 0150822 .oo.... 40 42 64 ( 77) 86..........= 02a0054 .....o. .......... 77 ( 86) 93..........+ 04410a8 2 ...o... .......... 86 ( 93) 102 103 104

= 0403880 * ...o... .......... 144 ( 89) 97 107.....

= 0412880 ..o.... .......... 144 ( 91) 100..........+ 0824100 ....o.. .......... 91 ( 100) 114..........+ 1148200 oo..... .......... 100 ( 114) 123..........

- 2 0228051 .....oo 71 72 73 ( 82) 95..........= 04500a2 ..o.... .......... 82 ( 95) 106..........+ 08a0144 2 ....o.. .......... 95 ( 106) 45 48 51

= 0502880 .o..... .......... 144 ( 96) 110..........+ 0a04110 ....oo. .......... 96 ( 110) 121..........

= 0806010 .....o. .......... 89 ( 97) 73..........

= 0906000 .o..... .......... 89 ( 107) 80..........

30

- 2 1508220 oo..... 80 83 110 ( 121) 127..........= 2a00540 ....o.. .......... 121 ( 127) 130..........+ 4410a80 2 ..o.... .......... 127 ( 130) 136 137 140

- 2 2280510 ....oo. 112 114 115 ( 123) 133..........= 4500a20 .o..... .......... 123 ( 133) 144..........+ 8a01440 2 ...o... .......... 133 ( 144) 89 91 96



31

8 WIDTH 8

Width 8

pg8 - zero component

pgg8 - examples

pggg8 - illustrated graph

ph8 - six isolated cycles

phh8 - packing filament pairs

pi8 - alpha component

pii8 - examples

piii8 - another example

pj8 - beta component tiles

pjj8 - beta de Bruijn diagram

pk8 - gamma component tiles

pkk8 - gamma de Bruijn diagram

pkkk8 - gamma example

pu8 - G’ph de Bruijn diagram

s.dat - full connection list

z.dat - zero component connections

maximum linkage: 3




zero: 19 33

alpha: 30 43

beta: 30 43

gamma: 56 86

+ 6 cycles: 6 6

337 nodes

411 links

10 components

32

Life Phoenix de Bruijn diagram, width 8


0

13

0

13

92

92

108

108

88

88

37

3752

52

178

178

150

28

28

150

33

33

45

45

69

69

73

73

78

78

153

153

154

154

89

91

89

91

zero component

19 nodes33 links

33

Life Phoenix de Bruijn diagram, width 8zero component

February 13, 1994pgg8.draw

178

1502837

52

178

1502837

52

178

15045

52

178

15045

52

2801392108

89

108

91

178

15028

34

88

7369

89

108

178

13

92

78

November 18, 1996pggg8.draw

15391

52

37

28

150

154

0

33

45

Life Phoenix de Bruijn diagram, width 8zero component

19 nodes33 links

35


February 11, 1994ph8.draw

6 isolated components

144

144

143

143

144

144

143

143

141

141

141

141

139

139

139

139

137

137

136

136

136

136

137

137

36

November 25, 1996

Only threealpha pairalignmentscan form aphoenix of

width 8;they

occupyseparateisolatedcycles.

(parallel strings)

(displaceddownward)

(displacedupward)

Only oneclose

pairingof alphaand betastrands

results in aphoenix; by

linkingwith other

gammastrands it

also gets tosit in thegamma

component.

(*)

phh8.draw

Lifephoenix

de Bruijndiagram,width 8

37



alpha component

23

23

3

3

5

38

6

39

6

39

206

206

149

165

149

29

29

213

165

244

248

244

38

277

277

290

290

298

299

299

298

315

325

315

325

60

103

60

11

11

19

94

94

289

289

237

257

237

257

43

43

129

190

129

190

5

103

31 nodes

19

248

213

38



alpha component

290298315

190

290298315

190

206

149

2935

39

206

149

2935

39

227244

213

103

227244

213

103

129

43

129

43

11

94

289

237

11

94

289

237

60

11

19

60

11

19

35

23

6

35

23

6

290298315

129

23

356

43

190

290298315

190257

277290

325

289

298

257

277290

325

289

298

39


alpha component

February 14, 1994piii8.draw

290298315

129

35

39

206

165

213227

244

60

11

94

289

257

277290

23

40


February 12, 1994pj8.draw

2

4

14

21

111

245

10

93

307

328

333

217

216

131

140

281

200

30

12 61

26

40

65

249

252320

251

326

beta component

200

326

281307333216

200

326

281307333216

214

93

307333217

214

93

307333217

131

26

131

26

30 tiles43 links

204

24

41


February 12, 1994pjj8.draw

beta component

sample loops

21421

111

245

1021421

111

245

10

30

12

61

30

12

61

30 tiles43 links

65

65

204

204

251

251

111

111

249

249

204

204

252

25210

10

2

2

4

4

24

24

2 4

14

24

26

93

21

111

249

245 10 307328 333131

140

216

217

200

281

320

326

40

12

30

61

204

251252

65

42


February 12, 1994pk8.draw

gamma component160

27

101

130

56

59

115

62

246

63

80

250

68

186

81

183

85

180

234

90

95

158

247

112

113

264

105

122

322

126

148

128

132

133

134

166

296

142

327

163

167

324

280

192

203

198

336

220

330

226

205

255

297

142

330

142

330

280297

324

280297

324

159

130

105

159

130

105

159

56 tiles

233

286

43


February 12, 1994pkk8.draw

gamma component

297

322

324

327

126

132

264

148

101

115

330

336

220

226

233

234

255

90 186 80

105

286

130

192

158

159

160

203

205

122

128

133

163

27

95 112113 198 246

247

250

166

167

63

183

68 180

56

59

62

81

85

134

56 tiles

280

296

142

44

pkkk8.draw February 13, 1994

Life Phoenix de Bruijn diagram, width 8gamma component130

158

115142

336220234186

205

133166198

246 63 80105

192

297

324

280297

324

280296

130158

128

205

142

142

336

280296

130158

115

233

128

128

205

205

133166198

198

247

246183205

324

322264

324

280297

336

226

336

286

233

280297

286

322264

226

336

286

286

297

233

280

327

286

286

336

336

128

205

122163112198

247

45

pu8.draw February 13, 1994

Life phoenix de Bruijn diagram

(width 8)

zero

alpha

beta

gamma

(beware - 236

is part of 108)

46


= 2 00000000 2 ........ 0 28 69 ( 0) 0 13 37

= 2 00001000 ....o... 0 28 69 ( 13) 92..........

+ 2 00103000 ..o.o... 13 33 73 ( 92) 108..........

- 0080c000 2 ........ .......... 125 ( 150) 28 33 45

= 00008000 2 ........ .......... 150 ( 28) 0 13 37

= 00009000 ....o... .......... 150 ( 33) 92..........

= 2 00010000 ...o.... 0 28 69 ( 37) 52..........

+ 2 00030100 ...o.o.. 37 45 78 ( 52) 178..........

= 00018000 ...o.... .......... 150 ( 45) 52..........

- 0081c000 ...o.... .......... 125 ( 154) 55..........= 00038100 ...o.o.. .......... 154 ( 55) 178..........

- 000c0800 2 ........ .......... 236 ( 88) 69 73 78

= 00080000 2 ........ .......... 88 ( 69) 0 13 37

= 00081000 ....o... .......... 88 ( 73) 92..........

= 00090000 ...o.... .......... 88 ( 78) 52..........

- 000d0800 ...o.... .......... 236 ( 91) 84..........= 000b0100 ...o.o.. .......... 91 ( 84) 178..........

= 000c1800 ....o... .......... 236 ( 89) 106..........+ 00183000 ..o.o... .......... 89 ( 106) 108..........

- 0080d000 ....o... .......... 125 ( 153) 97..........= 0010b000 ..o.o... .......... 153 ( 97) 108..........

- 2 01060200 .o...... 52 55 84 ( 178) 201..........= 020c0411 ......oo .......... 178 ( 201) 279..........+ 15080822 oo...... .......... 201 ( 279) 291..........+ 2a000054 ......o. .......... 279 ( 291) 300..........+ 441010a8 ..o.o... .......... 291 ( 300) 319..........+ 88203040 ....o... .......... 300 ( 319) 125..........+ 00406080 2 ........ .......... 319 ( 125) 150 153 154

- 2 00206010 ......o. 92 97 106 ( 108) 266..........- 1140c020 oo...... .......... 108 ( 266) 288..........

47

- 22808051 ......oo .......... 266 ( 288) 308..........- 450000a2 .o...... .......... 288 ( 308) 334..........- 8a010144 ...o.o.. .......... 308 ( 334) 218..........= 04030288 ...o.... .......... 334 ( 218) 236..........+ 08060400 2 ........ .......... 218 ( 236) 88 89 91


prospective tiles: 15- * 00004410 ......o. ..... 20 34 ( 23) 31..........- 00008820 ........ .......... 23 ( 31) 1..........= 00000051 ......oo .......... 31 ( 1) 3..........

+ * 000000a2 * ........ ..... 1 29 ( 3) 5 38.....

= 00000144 * .....o.. .......... 3 ( 5) 6 39.....

= 00000288 ........ .......... 5 ( 6) 17..........+ 00001500 ....oo.. .......... 6 ( 17) 20..........+ 00002a00 * ........ .......... 17 ( 20) 23 43.....

- * 00044100 .....o.. ..... 51 82 ( 60) 76..........- 00088200 ........ .......... 60 ( 76) 8..........= 00000510 .....oo. .......... 76 ( 8) 11..........

- * 00000a20 ........ ..... 8 70 ( 11) 16..........= 00001440 * ....o... .......... 11 ( 16) 19 94.....

= 00002880 ........ .......... 16 ( 19) 44..........+ 00015000 ...oo... .......... 19 ( 44) 51..........+ 0002a000 * ........ .......... 44 ( 51) 60 103.....

- * 00441000 ....o... ..... 118 168 ( 129) 157..........- 00882000 ........ .......... 129 ( 157) 25..........= 00005100 ....oo.. .......... 157 ( 25) 34..........+ 0000a200 * ........ .......... 25 ( 34) 23 43.....

= * 00008051 ......oo ..... 36 151 ( 29) 3..........

- 00806090 ......o. .......... 121 ( 149) 36..........= 0000c020 ........ .......... 149 ( 36) 29..........

= 00010144 ...o.o.. .......... 3 ( 38) 53..........+ 00030288 ...o.... .......... 38 ( 53) 179..........+ 01060400 .o...... .......... 53 ( 179) 202..........+ 020c0800 ........ .......... 179 ( 202) 277..........

+ * 15080000 oo...... ..... 199 202 ( 277) 290..........

= 00010388 ...o.o.. .......... 5 ( 39) 46..........+ 00020600 ........ .......... 39 ( 46) 184..........

48

+ 01140c11 .oo...oo .......... 46 ( 184) 206..........

= * 00014400 ...o.... ..... 20 34 ( 43) 50..........+ 00028800 ........ .......... 43 ( 50) 104..........+ 00150000 ..oo.... .......... 50 ( 104) 118..........+ 002a0000 * ........ .......... 104 ( 118) 129 190.....

- 08820000 ........ .......... 227 ( 244) 64..........= 00051000 ...oo... .......... 244 ( 64) 82..........+ 000a2000 * ........ .......... 64 ( 82) 60 103.....

- 08830100 ...o.o.. .......... 227 ( 248) 66..........= 00060200 ........ .......... 248 ( 66) 187..........+ 011c0411 .oo...oo .......... 66 ( 187) 206..........

- 08060900 .....o.. .......... 219 ( 237) 86..........- 000c0200 ........ .......... 237 ( 86) 70..........= 00080510 .....oo. .......... 86 ( 70) 11..........

= 00103880 ..o.o... .......... 16 ( 94) 107..........+ 00206000 ........ .......... 94 ( 107) 267..........+ 1140c110 oo...oo. .......... 107 ( 267) 289..........

= * 00144000 ..o..... ..... 51 82 ( 103) 117..........+ 00288000 ........ .......... 103 ( 117) 195..........+ 01500000 .oo..... .......... 117 ( 195) 213..........

+ * 02a00000 ........ ..... 195 196 ( 213) 227..........- 04410000 * ...o.... .......... 213 ( 227) 244 248.....

- 00906080 ..o..... .......... 121 ( 165) 110..........= 0020c000 ........ .......... 165 ( 110) 196..........+ 01508000 .oo..... .......... 110 ( 196) 213..........

- * 2a000000 * ........ ..... 272 277 ( 290) 298 299.....

- 44101000 ..o.o... .......... 290 ( 299) 318..........- 88203000 ....o... .......... 299 ( 318) 124..........= 00406010 ......o. .......... 318 ( 124) 151..........+ 0080c020 ........ .......... 124 ( 151) 29..........

- 44100000 * ..o..... .......... 290 ( 298) 315 325.....

- 88200000 ........ .......... 298 ( 315) 135..........= 00510000 ..oo.... .......... 315 ( 135) 168..........+ 00a20000 * ........ .......... 135 ( 168) 129 190.....

- 88301000 ..o.o... .......... 298 ( 325) 145..........= 00602000 ........ .......... 325 ( 145) 270..........+ 11c04110 oo...oo. .......... 145 ( 270) 289..........

49

= * 01440000 .o...... ..... 118 168 ( 190) 208..........+ 02880000 ........ .......... 190 ( 208) 272..........+ 15000000 oo...... .......... 208 ( 272) 290..........

- 09060800 .o...... .......... 219 ( 257) 199..........= 020c0000 ........ .......... 257 ( 199) 277..........

- * 02280822 ........ ..... 184 187 ( 206) 231..........= 04500054 ..o...o. .......... 206 ( 231) 253..........+ 08a010a8 ....o... .......... 231 ( 253) 121..........+ 00403040 * ....o... .......... 253 ( 121) 149 165.....

- * 22808220 ........ ..... 267 270 ( 289) 309..........= 45000540 .o...o.. .......... 289 ( 309) 335..........+ 8a010a80 ...o.... .......... 309 ( 335) 219..........+ 04030400 * ...o.... .......... 335 ( 219) 237 257.....



= * 00000054 * ......o. ..... 10 71 ( 2) 4 14.....

= 000000a8 ........ .......... 2 ( 4) 15..........+ 00001140 ....oo.. .......... 4 ( 15) 18..........+ 00002280 * ........ .......... 15 ( 18) 24 26.....

- * 00004500 .....o.. ..... 18 74 ( 24) 32..........- 00008a00 ........ .......... 24 ( 32) 7..........= 00000411 ......oo .......... 32 ( 7) 10..........

+ * 00000822 ........ ..... 7 72 ( 10) 2..........

- * 00008220 ........ ..... 22 152 ( 30) 9..........= 00000540 * .....o.. .......... 30 ( 9) 12 40.....

= 00000a80 ........ .......... 9 ( 12) 41..........+ 00011400 ...oo... .......... 12 ( 41) 48..........+ 00022800 * ........ .......... 41 ( 48) 61 65.....

= 000010a8 * ....o... .......... 2 ( 14) 21 93.....

= 00003040 ....o... .......... 14 ( 21) 96..........+ 00106090 ..o...o. .......... 21 ( 96) 111..........

- * 00045000 ....o... ..... 48 155 ( 61) 77..........- 0008a000 ........ .......... 61 ( 77) 22..........= 00004110 .....oo. .......... 77 ( 22) 30..........

= * 00005400 ....o... ..... 18 74 ( 26) 35..........+ 0000a800 ........ .......... 26 ( 35) 98..........

50

+ 00114000 ..oo.... .......... 35 ( 98) 114..........+ 00228000 * ........ .......... 98 ( 114) 131 140.....

= 00010a80 ...o.... .......... 9 ( 40) 54..........+ 00030400 ...o.... .......... 40 ( 54) 181..........+ 01060900 .o...o.. .......... 54 ( 181) 200..........

- 08820388 .....o.. .......... 228 ( 245) 57..........= 00040600 ........ .......... 245 ( 57) 72..........+ 00080c11 ......oo .......... 57 ( 72) 10..........

- * 00450000 ...o.... ..... 114 238 ( 131) 161..........- 008a0000 ........ .......... 131 ( 161) 58..........= 00041100 ....oo.. .......... 161 ( 58) 74..........+ 00082200 * ........ .......... 58 ( 74) 24 26.....

= * 00054000 ...o.... ..... 48 155 ( 65) 83..........+ 000a8000 ........ .......... 65 ( 83) 182..........+ 01140000 .oo..... .......... 83 ( 182) 204..........

- 08830288 ...o.... .......... 228 ( 249) 67..........= 00060400 ........ .......... 249 ( 67) 188..........+ 011c0800 .oo..... .......... 67 ( 188) 204..........

- 8a010000 * ...o.... .......... 307 ( 333) 216 217.....

- 04030100 ...o.o.. .......... 333 ( 217) 235..........- 08060200 ........ .......... 217 ( 235) 87..........- 000c0411 ......oo .......... 235 ( 87) 71..........= 00080822 ........ .......... 87 ( 71) 2..........

= 00103040 ..o.o... .......... 14 ( 93) 109..........+ 00206080 ........ .......... 93 ( 109) 265..........+ 1140c000 oo...... .......... 109 ( 265) 287..........+ 22808000 ........ .......... 265 ( 287) 307..........

+ * 45000000 * .o...... ..... 281 287 ( 307) 328 333.....

+ * 02280000 ........ ..... 182 188 ( 204) 230..........- 04500000 * ..o..... .......... 204 ( 230) 251 252.....

- 08a01000 ....o... .......... 230 ( 252) 120..........= 00403000 ....o... .......... 252 ( 120) 164..........+ 00906010 ..o...o. .......... 120 ( 164) 111..........

- 88203880 ....o... .......... 301 ( 320) 123..........= 00406000 ........ .......... 320 ( 123) 152..........+ 0080c110 .....oo. .......... 123 ( 152) 30..........

- 08a00000 ........ .......... 230 ( 251) 127..........= 00411000 ...oo... .......... 251 ( 127) 155..........

51

+ 00822000 * ........ .......... 127 ( 155) 61 65.....

= * 00540000 ..o..... ..... 114 238 ( 140) 173..........+ 00a80000 ........ .......... 140 ( 173) 259..........+ 11400000 oo...... .......... 173 ( 259) 281..........

+ * 22800000 ........ ..... 259 271 ( 281) 307..........

- 88302880 ..o..... .......... 301 ( 326) 146..........= 00604000 ........ .......... 326 ( 146) 271..........+ 11c08000 oo...... .......... 146 ( 271) 281..........

- * 0020c020 ........ ..... 96 164 ( 111) 197..........= 01508051 .oo...oo .......... 111 ( 197) 214..........+ 02a000a2 ........ .......... 197 ( 214) 228..........+ 04410144 * ...o.o.. .......... 214 ( 228) 245 249.....

= 04030000 ...o.... .......... 333 ( 216) 256..........+ 09060100 .o...o.. .......... 216 ( 256) 200..........

- 8a000000 ........ .......... 307 ( 328) 221..........= 04110000 ..oo.... .......... 328 ( 221) 238..........+ 08220000 * ........ .......... 221 ( 238) 131 140.....

- * 020c0200 ........ ..... 181 256 ( 200) 278..........= 15080510 oo...oo. .......... 200 ( 278) 292..........+ 2a000a20 ........ .......... 278 ( 292) 301..........+ 44101440 * ..o.o... .......... 292 ( 301) 320 326.....



- 00883040 * ....o... .......... 130 ( 160) 27 95.....

= 00006090 ......o. .......... 160 ( 27) 101..........

+ * 0011c020 ..oo.... ..... 27 148 ( 101) 115..........

- * 004410a8 2 ....o... ..... 119 170 ( 130) 158 159 160

- 00882140 .....o.. .......... 130 ( 159) 42..........= 00014280 ...o.... .......... 159 ( 42) 49..........+ 00028411 ......oo .......... 42 ( 49) 105..........

- 00040388 .....o.. .......... 162 ( 56) 79..........- 00090600 ...o.... .......... 56 ( 79) 47..........= 00020c11 ......oo .......... 79 ( 47) 105..........

= 00041288 ....o... .......... 162 ( 59) 75..........+ 00082410 ......o. .......... 59 ( 75) 100..........

52

+ 00114820 ..oo.... .......... 75 ( 100) 115..........

+ 2 00228051 * ......oo 99 100 101 ( 115) 132 142.....

= 00050288 2 ...o.... .......... 162 ( 62) 80 81 85

- 08820500 * .....o.. .......... 229 ( 246) 63 183.....

= 00050a00 ...o.... .......... 246 ( 63) 80..........

+ 2 000a0411 ......oo 62 63 90 ( 80) 105..........

- 08830400 * ...o.... .......... 229 ( 250) 68 180.....

= 00060900 .....o.. .......... 250 ( 68) 186..........

+ * 011c0200 .oo..... ..... 68 234 ( 186) 205..........

= 000a0500 .....o.. .......... 62 ( 81) 183..........

+ * 01140a00 .oo..... ..... 81 246 ( 183) 205..........

= 000b0400 ...o.... .......... 62 ( 85) 180..........

+ * 01060800 .o...... ..... 85 250 ( 180) 203..........

- 08060100 * .....o.. .......... 220 ( 234) 90 186.....

= 000d0200 ...o.... .......... 234 ( 90) 80..........

= 00106080 * ..o..... .......... 160 ( 95) 112 113.....

- 00882050 ......o. .......... 130 ( 158) 99..........= 001140a0 ..oo.... .......... 158 ( 99) 115..........

- 08821400 ....o... .......... 229 ( 247) 102..........= 00142800 ..o..... .......... 247 ( 102) 116..........+ 00284110 .....oo. .......... 102 ( 116) 198..........

= * 0020c110 .....oo. ..... 95 163 ( 112) 198..........

= 0020d000 ....o... .......... 95 ( 113) 264..........

+ 2 1140a000 oo...... 113 167 322 ( 264) 286..........

- 2 00150822 ..oo.... 47 49 80 ( 105) 119..........= 002a0054 * ......o. .......... 105 ( 119) 130 192.....

= 00403880 * ....o... .......... 254 ( 122) 148 163.....

- 88205000 2 ....o... .......... 306 ( 322) 126 134 264

53

= 0040b000 ....o... .......... 322 ( 126) 148..........

+ * 00806010 ......o. ..... 122 126 ( 148) 101..........

= 00412880 ...o.... .......... 254 ( 128) 156..........+ 00824100 .....o.. .......... 128 ( 156) 185..........+ 01148200 .oo..... .......... 156 ( 185) 205..........

= * 004500a2 ...o.... ..... 115 239 ( 132) 162..........+ 008a0144 2 .....o.. .......... 132 ( 162) 56 59 62

= 00502880 * ..o..... .......... 254 ( 133) 166 167.....

= 0050a000 ..o..... .......... 322 ( 134) 166..........

+ * 00a04110 .....oo. ..... 133 134 ( 166) 198..........

- * 2a004500 .....o.. ..... 275 280 ( 296) 305..........- 44108a00 ..o..... .......... 296 ( 305) 317..........- 88200411 ......oo .......... 305 ( 317) 138..........= 00510822 ..oo.... .......... 317 ( 138) 170..........+ 00a20054 * ......o. .......... 138 ( 170) 130 192.....

= * 005400a2 ..o..... ..... 115 239 ( 142) 176..........+ 00a80144 .....o.. .......... 142 ( 176) 261..........+ 11400288 oo...... .......... 176 ( 261) 283..........+ 22801500 ....oo.. .......... 261 ( 283) 311..........+ 45002a00 * .o...... .......... 283 ( 311) 330 336.....

- 88304000 ..o..... .......... 306 ( 327) 147..........= 00609000 ....o... .......... 327 ( 147) 269..........+ 11c02000 oo...... .......... 147 ( 269) 286..........

= 00906000 ..o..... .......... 122 ( 163) 112..........

= 00a05000 ....o... .......... 133 ( 167) 264..........

- 88214000 ...o.... .......... 306 ( 324) 189..........= 01428000 .o...... .......... 324 ( 189) 207..........+ 02841100 ....oo.. .......... 189 ( 207) 280..........

+ 2 15082200 * oo...... 203 207 258 ( 280) 296 297.....

= * 014400a8 .o...... ..... 119 170 ( 192) 211..........+ 02881140 ....oo.. .......... 192 ( 211) 275..........+ 15002280 * oo...... .......... 211 ( 275) 296 297.....

= * 020c1100 ....oo.. ..... 180 255 ( 203) 280..........

- 2 01508220 .oo..... 112 116 166 ( 198) 215..........

54

= 02a00540 .....o.. .......... 198 ( 215) 229..........+ 04410a80 2 ...o.... .......... 215 ( 229) 246 247 250

- * 8a014400 2 ...o.... ..... 311 314 ( 336) 220 226 233

= 04038800 * ...o.... .......... 336 ( 220) 234 255.....

- * 8a004410 ......o. ..... 311 314 ( 330) 224..........= 04118820 ..oo.... .......... 330 ( 224) 239..........+ 08220051 * ......oo .......... 224 ( 239) 132 142.....

= 04128800 ..o..... .......... 336 ( 226) 243..........+ 08241000 ....o... .......... 226 ( 243) 268..........+ 11482000 oo...... .......... 243 ( 268) 286..........

- 2 02280510 .....oo. 183 185 186 ( 205) 232..........= 04500a20 ..o..... .......... 205 ( 232) 254..........+ 08a01440 2 ....o... .......... 232 ( 254) 122 128 133

= 05028800 .o...... .......... 336 ( 233) 258..........+ 0a041100 ....oo.. .......... 233 ( 258) 280..........

= 09060000 .o...... .......... 220 ( 255) 203..........

= * 2a005400 ....o... ..... 275 280 ( 297) 306..........+ 4410a800 2 ..o..... .......... 297 ( 306) 322 324 327

- 2 22805100 ....oo.. 264 268 269 ( 286) 314..........= 4500a200 * .o...... .......... 286 ( 314) 330 336.....


prospective tiles: 104- 00510051 ..oo..oo .......... 323 ( 136) 171..........- 00a200a2 ........ .......... 136 ( 171) 193..........- 01440144 .o...o.. .......... 171 ( 193) 210..........- 02880288 ........ .......... 193 ( 210) 274..........- 15001500 oo..oo.. .......... 210 ( 274) 294..........- 2a002a00 ........ .......... 274 ( 294) 303..........- 44104410 ..o...o. .......... 294 ( 303) 323..........- 88208820 ........ .......... 303 ( 323) 136..........= 00510051 ..oo..oo .......... 323 ( 136) 171..........


prospective tiles: 105- 005100a2 ..oo.... .......... 316 ( 137) 172..........- 00a20144 .....o.. .......... 137 ( 172) 194..........- 01440288 .o...... .......... 172 ( 194) 212..........- 02881500 ....oo.. .......... 194 ( 212) 276..........- 15002a00 oo...... .......... 212 ( 276) 295..........

55

- 2a004410 ......o. .......... 276 ( 295) 304..........- 44108820 ..o..... .......... 295 ( 304) 316..........- 88200051 ......oo .......... 304 ( 316) 137..........= 005100a2 ..oo.... .......... 316 ( 137) 172..........


prospective tiles: 106- 00518820 ..oo.... .......... 321 ( 139) 169..........- 00a20051 ......oo .......... 139 ( 169) 191..........- 014400a2 .o...... .......... 169 ( 191) 209..........- 02880144 .....o.. .......... 191 ( 209) 273..........- 15000288 oo...... .......... 209 ( 273) 293..........- 2a001500 ....oo.. .......... 273 ( 293) 302..........- 44102a00 ..o..... .......... 293 ( 302) 321..........- 88204410 ......o. .......... 302 ( 321) 139..........= 00518820 ..oo.... .......... 321 ( 139) 169..........


prospective tiles: 107- 00540054 ..o...o. .......... 242 ( 141) 175..........- 00a800a8 ........ .......... 141 ( 175) 262..........- 11401140 oo..oo.. .......... 175 ( 262) 284..........- 22802280 ........ .......... 262 ( 284) 312..........- 45004500 .o...o.. .......... 284 ( 312) 332..........- 8a008a00 ........ .......... 312 ( 332) 222..........- 04110411 ..oo..oo .......... 332 ( 222) 242..........- 08220822 ........ .......... 222 ( 242) 141..........= 00540054 ..o...o. .......... 242 ( 141) 175..........


prospective tiles: 108- 005400a8 ..o..... .......... 240 ( 143) 177..........- 00a81140 ....oo.. .......... 143 ( 177) 263..........- 11402280 oo...... .......... 177 ( 263) 285..........- 22804500 .....o.. .......... 263 ( 285) 313..........- 45008a00 .o...... .......... 285 ( 313) 329..........- 8a000411 ......oo .......... 313 ( 329) 223..........- 04110822 ..oo.... .......... 329 ( 223) 240..........- 08220054 ......o. .......... 223 ( 240) 143..........= 005400a8 ..o..... .......... 240 ( 143) 177..........


prospective tiles: 109- 00540822 ..o..... .......... 241 ( 144) 174..........- 00a80054 ......o. .......... 144 ( 174) 260..........- 114000a8 oo...... .......... 174 ( 260) 282..........- 22801140 ....oo.. .......... 260 ( 282) 310..........

56

- 45002280 .o...... .......... 282 ( 310) 331..........- 8a004500 .....o.. .......... 310 ( 331) 225..........- 04118a00 ..oo.... .......... 331 ( 225) 241..........- 08220411 ......oo .......... 225 ( 241) 144..........= 00540822 ..o..... .......... 241 ( 144) 174..........



57

Width 8 - z.dat Zero component connections

= 2 00000000 2 ........ 0 28 69 ( 0) 0 13 37

= 2 00001000 ....o... 0 28 69 ( 13) 92..........

+ 2 00103000 ..o.o... 13 33 73 ( 92) 108..........

- 0080c000 2 ........ .......... 125 ( 150) 28 33 45

= 00008000 2 ........ .......... 150 ( 28) 0 13 37

= 00009000 ....o... .......... 150 ( 33) 92..........

= 2 00010000 ...o.... 0 28 69 ( 37) 52..........

+ 2 00030100 ...o.o.. 37 45 78 ( 52) 178..........

= 00018000 ...o.... .......... 150 ( 45) 52..........

- 0081c000 ...o.... .......... 125 ( 154) 55..........= 00038100 ...o.o.. .......... 154 ( 55) 178..........

- 000c0800 2 ........ .......... 236 ( 88) 69 73 78

= 00080000 2 ........ .......... 88 ( 69) 0 13 37

= 00081000 ....o... .......... 88 ( 73) 92..........

= 00090000 ...o.... .......... 88 ( 78) 52..........

- 000d0800 ...o.... .......... 236 ( 91) 84..........= 000b0100 ...o.o.. .......... 91 ( 84) 178..........

= 000c1800 ....o... .......... 236 ( 89) 106..........+ 00183000 ..o.o... .......... 89 ( 106) 108..........

- 0080d000 ....o... .......... 125 ( 153) 97..........= 0010b000 ..o.o... .......... 153 ( 97) 108..........

- 2 01060200 .o...... 52 55 84 ( 178) 201..........= 020c0411 ......oo .......... 178 ( 201) 279..........+ 15080822 oo...... .......... 201 ( 279) 291..........+ 2a000054 ......o. .......... 279 ( 291) 300..........+ 441010a8 ..o.o... .......... 291 ( 300) 319..........+ 88203040 ....o... .......... 300 ( 319) 125..........+ 00406080 2 ........ .......... 319 ( 125) 150 153 154

- 2 00206010 ......o. 92 97 106 ( 108) 266..........- 1140c020 oo...... .......... 108 ( 266) 288..........

58

- 22808051 ......oo .......... 266 ( 288) 308..........- 450000a2 .o...... .......... 288 ( 308) 334..........- 8a010144 ...o.o.. .......... 308 ( 334) 218..........= 04030288 ...o.... .......... 334 ( 218) 236..........+ 08060400 2 ........ .......... 218 ( 236) 88 89 91


59

9 WIDTH 9

Width 9

pg9 - zero component

pgg9 - de Bruijn diagram

pggg9 - examples

ph9 - some isolated components

phh9 - examples

phhh9 - counting filament pairs

pi9 - middle component #1

pii9 - middle component #2

pj9 - alpha component tiles

pjj9 - alpha de Bruijn diagram

pjjj9 - alpha exampls

pk9 - beta component tiles

pkk9 - beta de Bruijn diagram

pkkk9 - beta examples

pkkkk9 - more beta examples

pl9 - gamma component tiles

pll9 - gamma de Bruijn diagram

s.dat - full linkage list

z.dat - zero linkage list

818 nodes

970 links

44 components

maximum linkage: 4


consolidated links:


zero: 48

alpha: 50

beta: 50

gamma: 88

medium: 6

medium: 6

+ 38 cycles: 38

60



zero component48 nodes

114

399

237

213

13

94

99

112

166

329

186

204

88

37

92

12652

17073

181

78

153

333

205161

174

208

209

331

33

28

45

171

55

0 69

84

91

89

111

110

217

131

334

206

160

235

211

61




13

88

37

52

2833

45

69

73

78

237 114

213399

94

84

91

92

16699

110

126

112

186

160

161204

170174

181

205

208 209

211

217

333

329

331

1690

131

334

206

235 89

111

171

55

62


February 23, 1994pggg9.draw

zero component

0003752

213

186

399

3296900

00

130

94114

89111114

88110126399

32969000

213

171211237

206

174

213

171211237

206

174

63



isolated cycles

321

321

321

321

302

302 302

302

(38 altogether)

64

Life phoenix de Bruijn diagram, width 938 isolated cycles

phh9.draw November 20, 1996

The smallest phoenix avatars occupy 2x4 rectangles which canbe strung out into strands whose central glide axis makes for a4x8 unit cell. Given wider space, they can twist and turn, butthere will always be a family of phoenices comprised of perfectlystraight parallel filaments. Individual strings can be pairedaccording to their phase, given that alternate generations arereflections in a mirror perpendicular to the glide axis, and thusdistinct from one another.

The closest packing is to crowd a pair of filaments in a columnof width 8, wherein just three relative displacements of the samephase are free from interference. With opposite phases, only onepossibility arises, but it takes its place in the gamma component.

Wider spacing allows any of eight alignments, of either relativephase.

Besides the two subdiagrams of width 8, one left clinging, theother right clinging, further possibilities arise in the strip of width9 when the two strands cling to opposite walls, for which thereare no packing problems and all eight relative displacementscan occur, moreover each for both relative phases between thestrands.

This would all seem to add up to 44 different arrangements, 32 offull width 9, 6 of embedded width 8 on the left, and 6 more on theright. Six of this total, precisely the most symmetric ones, are lostto enlarged alpha (1), beta (1), and middle (4) components,leaving the remaining 38 in isolated cycles.

65

749

303

749

303

600

806

600

806

305

798

305

798

424

720

424

720

283

695

283

695

422

692

422

692


November 25, 1996phhh9.draw

alpha beta

middle

middle

Parallel filament pairswhich incorporate intoother components ratherthan just isolated cycles.

66



305

806

798

814

621

600

600

814

798

806

305

621

middle components 600

806

600

814

798

621

600

806

600

806

621

798

814

600

(2 total)

67



middle components(2 total)

283

695

692

422

700 416

283

692

416

700

422

695

68

November 19,1996

Life phoenix de Bruijn diagram, width 9alpha component

pj9.draw

50 nodes23

3

5

6

60

11

16

19

141

34

29

164

38

445

39

247

43

50

487

524

570

226

681

707

760

419

272

341

107

254

345

70

328

93

649

96

185

525

580

545

212

679

354

724

276

303

788

594

749

462

750

69


50 nodes

November 22, 1996pjj9.draw

3

5

38

6

39

23

43

212

50

141

226

34

487

524

525

570

580

29 164 445247

679

11

1619 96107

60272

70

328

93

649

462

254419681

707

724

760

788

749

750

354

545

594

276

303

185

341

70


50 nodes

pjjj9.draw November 23, 1996

487525

29338

445487525

29338

445

487524570

141

344350

226

487524570

141

344350

226

707681

788

679750

594

649

707681

788

679750

594

649487524570

226

487524570

226

71

November 19, 1996

Life phoenix de Bruijn diagram, width 9beta component

pk9.draw

2

24

10

9

4

30

40

21

54

273

342

74

245

588

258

95

533

26

275

454

812

496

210

734

257

726

720

654

424

240

495

791

301

12

61

65

450

143

349

346

100

348

575

581

152

117

781

789

50 nodes

35

583

72


pkk9.draw November 19, 1996

789

654

734

791 812

275

301

348

349

495

496

9

12 40

61

65

30

245

54

210

240

117

273

424450

726

720

575

581

342

346

2

4

14

24

26

10

35

100

143

152

74

454 533

583588

95

21

257

258

781

beta component50 nodes

73


November 19, 1996pkkk9.draw

789

654734791

301

654734812496

912

61

309

65

12

245275348

24

24

1024

24

10

26

143

7426

143

74

35

35

152

454533583

152

454533583

789

654734791

301

654734791

12

61

30912

61

9

30

275348

65

245

275348

65

245


74

424

720

424

720

726

424

789

654734791

301

654734812495

450

720

720

November 20, 1996pkkkk9.draw


240

581

454533588257

240

581

454533588257

24

2635

152

454533583

143

7424

102


720

273342

1024

26100

450

720

75

November 19, 1996


pl9.draw

gamma component178

27

142

177

56

59

121

62

343

63

80

347

68

222

81

219

85

215

325

90

97

176

274

344

118

119

408

109

130

401

577

134

138

163

140

246

144

146

187

154

493

582

159

413

183

145

188

200

542

202

207

579

448

228

243

244

617

234

591

261

783

265

585

271

277

278

279

355

704

311

790

352

356

785

653

429

453

494

816

499

809

522

459

541

592

705

676

88 nodes

105

76

Life phoenix de Bruijn diagram, width 9gamma component

88 nodes

November 20, 1996pll9.draw

178

154

704

585

591

144

274

429

705790676

816

493

142

228

494

311

809

277

522

541

499

653

542

592 453

202

207

413

134

140

145

783

785

459

617

356

271

261

278

188

200

343

344

34768

215

163

183

63

219

234187

118

408 577

138

146

579

582

176121

27

97

56

59

62 80

81

85

355

325

352

90

222

109

246

243

448

159

401

105

244265

279

355

130

119

177

77

Width 9 - s.dat Full linkage list

= 3 000000000 3 ......... 0 28 69 160 ( 0) 0 13 37 92

= 3 000001000 .....o... 0 28 69 160 ( 13) 94...............

+ 3 000103000 ...o.o... 13 33 73 161 ( 94) 114...............

- 00080c000 3 ......... ............... 137 ( 166) 28 33 45 99

= 000008000 3 ......... ............... 166 ( 28) 0 13 37 92

= 000009000 .....o... ............... 166 ( 33) 94...............

= 3 000010000 * ....o.... 0 28 69 160 ( 37) 52 209..........

= 000018000 * ....o.... ............... 166 ( 45) 52 209..........

= 3 000030100 ....o.o.. 37 45 78 170 ( 52) 213...............

- 00081c000 * ....o.... ............... 137 ( 171) 55 211..........

= 000038100 ....o.o.. ............... 171 ( 55) 213...............

= * 000080000 3 ......... .......... 88 329 ( 69) 0 13 37 92

= * 000081000 .....o... .......... 88 329 ( 73) 94...............

= * 000090000 * ....o.... .......... 88 329 ( 78) 52 209..........

= * 0000b0100 ....o.o.. .......... 91 333 ( 84) 213...............

= 0000c0800 3 ......... ............... 327 ( 88) 69 73 78 110

= 0000c1800 .....o... ............... 327 ( 89) 111...............

+ * 000183000 ...o.o... .......... 89 331 ( 111) 114...............

= 0000d0800 * ....o.... ............... 327 ( 91) 84 217..........

= 3 000100000 ...o..... 0 28 69 160 ( 92) 126...............

+ 3 000301000 ...o.o... 92 99 110 181 ( 126) 399...............

= 000108000 ...o..... ............... 166 ( 99) 126...............

- 00080d000 .....o... ............... 137 ( 169) 101...............= 00010b000 ...o.o... ............... 169 ( 101) 114...............

= * 000180000 ...o..... .......... 88 329 ( 110) 126...............

78

= 0001c0800 ...o..... ............... 327 ( 112) 131...............

+ * 000381000 ...o.o... .......... 112 334 ( 131) 399...............

- 00090c000 ...o..... ............... 137 ( 186) 129...............= 000309000 ...o.o... ............... 186 ( 129) 399...............

- 000c08000 3 ......... ............... 544 ( 204) 160 161 170 181

= 000800000 3 ......... ............... 204 ( 160) 0 13 37 92

= 000801000 .....o... ............... 204 ( 161) 94...............

= 000810000 * ....o.... ............... 204 ( 170) 52 209..........

- 000c18000 * ....o.... ............... 544 ( 206) 174 235..........

= 000830100 ....o.o.. ............... 206 ( 174) 213...............

= 000900000 ...o..... ............... 204 ( 181) 126...............

- 000c09000 .....o... ............... 544 ( 205) 182...............= 000903000 ...o.o... ............... 205 ( 182) 114...............

- 000d08000 ...o..... ............... 544 ( 208) 199...............= 000b01000 ...o.o... ............... 208 ( 199) 399...............

= 3 001030000 ..o.o.... 37 45 78 170 ( 209) 237...............

= 001038000 ..o.o.... ............... 171 ( 211) 237...............

= * 0010b0000 ..o.o.... .......... 91 333 ( 217) 237...............

= 001830000 ..o.o.... ............... 206 ( 235) 237...............

- 3 001060200 ..o...... 52 55 84 174 ( 213) 241...............= 0020c0411 .......oo ............... 213 ( 241) 447...............+ 015080822 .oo...... ............... 241 ( 447) 488...............+ 02a000054 .......o. ............... 447 ( 488) 526...............+ 0441010a8 ...o.o... ............... 488 ( 526) 574...............+ 088203040 .....o... ............... 526 ( 574) 137...............+ 000406080 3 ......... ............... 574 ( 137) 166 169 171 186

- 3 000206010 .......o. 94 101 111 182 ( 114) 410...............- 01140c020 .oo...... ............... 114 ( 410) 461...............- 022808051 .......oo ............... 410 ( 461) 534...............- 0450000a2 ..o...... ............... 461 ( 534) 589...............- 08a010144 ....o.o.. ............... 534 ( 589) 259...............= 004030288 ....o.... ............... 589 ( 259) 327...............+ 008060400 3 ......... ............... 259 ( 327) 88 89 91 112

79

- 3 010602000 .o....... 126 129 131 199 ( 399) 451...............- 020c04110 ......oo. ............... 399 ( 451) 651...............- 150808220 oo....... ............... 451 ( 651) 689...............- 2a0000540 ......o.. ............... 651 ( 689) 725...............- 441010a80 ..o.o.... ............... 689 ( 725) 780...............- 882030400 ....o.... ............... 725 ( 780) 264...............= 004060800 3 ......... ............... 780 ( 264) 329 331 333 334

= 0080c0000 3 ......... ............... 264 ( 329) 69 73 78 110

= 0080c1000 .....o... ............... 264 ( 331) 111...............

= 0080d0000 * ....o.... ............... 264 ( 333) 84 217..........

= 0081c0000 ...o..... ............... 264 ( 334) 131...............

- 3 002060100 ......o.. 209 211 217 235 ( 237) 619...............- 1140c0200 oo....... ............... 237 ( 619) 678...............- 228080510 ......oo. ............... 619 ( 678) 743...............- 450000a20 .o....... ............... 678 ( 743) 813...............- 8a0101440 ...o.o... ............... 743 ( 813) 497...............= 040302880 ...o..... ............... 813 ( 497) 544...............+ 080604000 3 ......... ............... 497 ( 544) 204 205 206 208



- * 000004410 .......o. .......... 20 34 ( 23) 31...............- 000008820 ......... ............... 23 ( 31) 1...............= 000000051 .......oo ............... 31 ( 1) 3...............

+ * 0000000a2 * ......... .......... 1 29 ( 3) 5 38..........

= 000000144 * ......o.. ............... 3 ( 5) 6 39..........

= 000000288 ......... ............... 5 ( 6) 17...............+ 000001500 .....oo.. ............... 6 ( 17) 20...............+ 000002a00 * ......... ............... 17 ( 20) 23 43..........

- * 000044100 ......o.. .......... 51 82 ( 60) 76...............- 000088200 ......... ............... 60 ( 76) 8...............= 000000510 ......oo. ............... 76 ( 8) 11...............

+ * 000000a20 * ......... .......... 8 70 ( 11) 16 93..........

= 000001440 * .....o... ............... 11 ( 16) 19 96..........

= 000002880 ......... ............... 16 ( 19) 44...............+ 000015000 ....oo... ............... 19 ( 44) 51...............

80

+ 00002a000 * ......... ............... 44 ( 51) 60 107..........

- * 000441000 .....o... .......... 124 189 ( 141) 175...............- 000882000 ......... ............... 141 ( 175) 25...............= 000005100 .....oo.. ............... 175 ( 25) 34...............

+ * 00000a200 * ......... .......... 25 162 ( 34) 23 43..........

= * 000008051 .......oo .......... 36 167 ( 29) 3...............

- 000806090 .......o. ............... 133 ( 164) 36...............= 00000c020 ......... ............... 164 ( 36) 29...............

= 000010144 ....o.o.. ............... 3 ( 38) 53...............+ 000030288 ....o.... ............... 38 ( 53) 214...............+ 001060400 ..o...... ............... 53 ( 214) 242...............+ 0020c0800 ......... ............... 214 ( 242) 445...............

+ * 015080000 .oo...... .......... 239 242 ( 445) 487...............

= 000010388 ....o.o.. ............... 5 ( 39) 46...............+ 000020600 ......... ............... 39 ( 46) 220...............+ 001140c11 ..oo...oo ............... 46 ( 220) 247...............

+ * 002280822 * ......... .......... 220 223 ( 247) 276 303..........

= * 000014400 * ....o.... .......... 20 34 ( 43) 50 212..........

= 000028800 ......... ............... 43 ( 50) 108...............+ 000150000 ...oo.... ............... 50 ( 108) 124...............+ 0002a0000 * ......... ............... 108 ( 124) 141 226..........

- * 004410000 * ....o.... .......... 254 357 ( 272) 341 345..........

- 008820000 ......... ............... 272 ( 341) 64...............= 000051000 ....oo... ............... 341 ( 64) 82...............+ 0000a2000 * ......... ............... 64 ( 82) 60 107..........

- 008830100 ....o.o.. ............... 272 ( 345) 66...............= 000060200 ......... ............... 345 ( 66) 223...............+ 0011c0411 ..oo...oo ............... 66 ( 223) 247...............

= * 000080510 ......oo. .......... 86 330 ( 70) 11...............

- 008060900 ......o.. ............... 260 ( 328) 86...............= 0000c0200 ......... ............... 328 ( 86) 70...............

= 000101440 ...o.o... ............... 11 ( 93) 127...............+ 000302880 ...o..... ............... 93 ( 127) 400...............+ 010604000 .o....... ............... 127 ( 400) 452...............+ 020c08000 ......... ............... 400 ( 452) 649...............

81

+ * 150800000 oo....... .......... 449 452 ( 649) 681...............

= 000103880 ...o.o... ............... 16 ( 96) 113...............+ 000206000 ......... ............... 96 ( 113) 411...............+ 01140c110 .oo...oo. ............... 113 ( 411) 462...............

= * 000144000 ...o..... .......... 51 82 ( 107) 123...............+ 000288000 ......... ............... 107 ( 123) 231...............+ 001500000 ..oo..... ............... 123 ( 231) 254...............

+ * 002a00000 * ......... .......... 231 232 ( 254) 272 419..........

- 000906080 ...o..... ............... 133 ( 185) 116...............= 00020c000 ......... ............... 185 ( 116) 232...............+ 001508000 ..oo..... ............... 116 ( 232) 254...............

- * 02a000000 * ......... .......... 440 445 ( 487) 524 525..........

- 044101000 ...o.o... ............... 487 ( 525) 573...............- 088203000 .....o... ............... 525 ( 573) 136...............= 000406010 .......o. ............... 573 ( 136) 167...............+ 00080c020 ......... ............... 136 ( 167) 29...............

- 044100000 * ...o..... ............... 487 ( 524) 570 580..........

- 088200000 ......... ............... 524 ( 570) 147...............= 000510000 ...oo.... ............... 570 ( 147) 189...............+ 000a20000 * ......... ............... 147 ( 189) 141 226..........

- 088301000 ...o.o... ............... 524 ( 580) 157...............= 000602000 ......... ............... 580 ( 157) 414...............+ 011c04110 .oo...oo. ............... 157 ( 414) 462...............

- 080609000 .....o... ............... 498 ( 545) 201...............- 000c02000 ......... ............... 545 ( 201) 162...............= 000805100 .....oo.. ............... 201 ( 162) 34...............

= 001038800 ..o.o.... ............... 43 ( 212) 236...............+ 002060000 ......... ............... 212 ( 236) 620...............+ 1140c1100 oo...oo.. ............... 236 ( 620) 679...............

+ * 228082200 * ......... .......... 620 625 ( 679) 749 750..........

= * 001440000 ..o...... .......... 124 189 ( 226) 249...............+ 002880000 ......... ............... 226 ( 249) 440...............+ 015000000 .oo...... ............... 249 ( 440) 487...............

- 009060800 ..o...... ............... 260 ( 354) 239...............= 0020c0000 ......... ............... 354 ( 239) 445...............

82

- * 2a0000000 * ......... .......... 627 649 ( 681) 707 724..........

- 441010000 ..o.o.... ............... 681 ( 724) 779...............- 882030000 ....o.... ............... 724 ( 779) 263...............= 004060100 ......o.. ............... 779 ( 263) 330...............+ 0080c0200 ......... ............... 263 ( 330) 70...............

= * 004500054 ...o...o. .......... 247 556 ( 276) 350...............+ 008a010a8 .....o... ............... 276 ( 350) 133...............+ 000403040 * .....o... ............... 350 ( 133) 164 185..........

- 441000000 * ..o...... ............... 681 ( 707) 760 788..........

- 882000000 ......... ............... 707 ( 760) 280...............= 005100000 ..oo..... ............... 760 ( 280) 357...............+ 00a200000 * ......... ............... 280 ( 357) 272 419..........

= * 005400054 ..o....o. .......... 247 556 ( 303) 382...............+ 00a8000a8 ......... ............... 303 ( 382) 606...............+ 114001140 oo...oo.. ............... 382 ( 606) 665...............+ 228002280 * ......... ............... 606 ( 665) 749 750..........

- 883010000 ..o.o.... ............... 707 ( 788) 322...............= 006020000 ......... ............... 788 ( 322) 625...............+ 11c041100 oo...oo.. ............... 322 ( 625) 679...............

= * 014400000 .o....... .......... 254 357 ( 419) 466...............+ 028800000 ......... ............... 419 ( 466) 627...............+ 150000000 oo....... ............... 466 ( 627) 681...............

- 090608000 .o....... ............... 498 ( 594) 449...............= 020c00000 ......... ............... 594 ( 449) 649...............

- * 450004500 .o....o.. .......... 665 679 ( 749) 808...............- 8a0008a00 ......... ............... 749 ( 808) 507...............= 041100411 ..oo...oo ............... 808 ( 507) 556...............+ 082200822 * ......... ............... 507 ( 556) 276 303..........

- * 022808220 ......... .......... 411 414 ( 462) 535...............= 045000540 ..o...o.. ............... 462 ( 535) 590...............+ 08a010a80 ....o.... ............... 535 ( 590) 260...............+ 004030400 * ....o.... ............... 590 ( 260) 328 354..........

= * 450005400 .o...o... .......... 665 679 ( 750) 815...............+ 8a010a800 ...o..... ............... 750 ( 815) 498...............+ 040304000 * ...o..... ............... 815 ( 498) 545 594..........



83

= * 000000054 * .......o. .......... 10 71 ( 2) 4 14..........

= 0000000a8 ......... ............... 2 ( 4) 15...............+ 000001140 .....oo.. ............... 4 ( 15) 18...............+ 000002280 * ......... ............... 15 ( 18) 24 26..........

- * 000004500 ......o.. .......... 18 74 ( 24) 32...............- 000008a00 ......... ............... 24 ( 32) 7...............= 000000411 .......oo ............... 32 ( 7) 10...............

+ * 000000822 ......... .......... 7 72 ( 10) 2...............

= * 000000540 * ......o.. .......... 30 165 ( 9) 12 40..........

= 000000a80 ......... ............... 9 ( 12) 41...............+ 000011400 ....oo... ............... 12 ( 41) 48...............+ 000022800 * ......... ............... 41 ( 48) 61 65..........

= 000003040 .....o... ............... 14 ( 21) 98...............+ 000106090 ...o...o. ............... 21 ( 98) 117...............

- * 000045000 .....o... .......... 48 172 ( 61) 77...............- 00008a000 ......... ............... 61 ( 77) 22...............= 000004110 ......oo. ............... 77 ( 22) 30...............

+ * 000008220 ......... .......... 22 168 ( 30) 9...............

= 00000a800 ......... ............... 26 ( 35) 102...............+ 000114000 ...oo.... ............... 35 ( 102) 120...............+ 000228000 * ......... ............... 102 ( 120) 143 152..........

= 000010a80 * ....o.... ............... 9 ( 40) 54 210..........

= 000030400 ....o.... ............... 40 ( 54) 216...............+ 001060900 ..o...o.. ............... 54 ( 216) 240...............

- * 004410144 * ....o.o.. .......... 255 360 ( 273) 342 346..........

- 008820388 ......o.. ............... 273 ( 342) 57...............= 000040600 ......... ............... 342 ( 57) 72...............+ 000080c11 .......oo ............... 57 ( 72) 10...............

- * 000450000 ....o.... .......... 120 335 ( 143) 179...............- 0008a0000 ......... ............... 143 ( 179) 58...............= 000041100 .....oo.. ............... 179 ( 58) 74...............

+ * 000082200 * ......... .......... 58 332 ( 74) 24 26..........

= * 000054000 ....o.... .......... 48 172 ( 65) 83...............+ 0000a8000 ......... ............... 65 ( 83) 218...............+ 001140000 ..oo..... ............... 83 ( 218) 245...............

84

+ * 002280000 * ......... .......... 218 224 ( 245) 275 301..........

- 008830288 ....o.... ............... 273 ( 346) 67...............= 000060400 ......... ............... 346 ( 67) 224...............+ 0011c0800 ..oo..... ............... 67 ( 224) 245...............

- 08a010000 * ....o.... ............... 533 ( 588) 257 258..........

- 004030100 ....o.o.. ............... 588 ( 258) 326...............- 008060200 ......... ............... 258 ( 326) 87...............- 0000c0411 .......oo ............... 326 ( 87) 71...............= 000080822 ......... ............... 87 ( 71) 2...............

- 0000010a8 * .....o... ............... 2 ( 14) 21 95..........

= 000103040 ...o.o... ............... 14 ( 95) 115...............+ 000206080 ......... ............... 95 ( 115) 409...............+ 01140c000 .oo...... ............... 115 ( 409) 460...............+ 022808000 ......... ............... 409 ( 460) 533...............

+ * 045000000 * ..o...... .......... 454 460 ( 533) 583 588..........

- * 000005400 * .....o... .......... 18 74 ( 26) 35 100..........

= 00010a800 ...o..... ............... 26 ( 100) 128...............+ 000304000 ...o..... ............... 100 ( 128) 402...............+ 010609000 .o...o... ............... 128 ( 402) 450...............

- * 004500000 * ...o..... .......... 245 546 ( 275) 348 349..........

- 008a01000 .....o... ............... 275 ( 349) 132...............= 000403000 .....o... ............... 349 ( 132) 184...............+ 000906010 ...o...o. ............... 132 ( 184) 117...............

- 088203880 .....o... ............... 527 ( 575) 135...............= 000406000 ......... ............... 575 ( 135) 168...............+ 00080c110 ......oo. ............... 135 ( 168) 30...............

- 008a00000 ......... ............... 275 ( 348) 139...............= 000411000 ....oo... ............... 348 ( 139) 172...............+ 000822000 * ......... ............... 139 ( 172) 61 65..........

= * 000540000 ...o..... .......... 120 335 ( 152) 194...............+ 000a80000 ......... ............... 152 ( 194) 403...............+ 011400000 .oo...... ............... 194 ( 403) 454...............

+ * 022800000 ......... .......... 403 415 ( 454) 533...............

- 088302880 ...o..... ............... 527 ( 581) 158...............= 000604000 ......... ............... 581 ( 158) 415...............

85

+ 011c08000 .oo...... ............... 158 ( 415) 454...............

- 8a0100000 * ...o..... ............... 734 ( 812) 495 496..........

- 040301000 ...o.o... ............... 812 ( 496) 543...............- 080602000 ......... ............... 496 ( 543) 203...............- 000c04110 ......oo. ............... 543 ( 203) 165...............= 000808220 ......... ............... 203 ( 165) 9...............

= 001030400 ..o.o.... ............... 40 ( 210) 238...............+ 002060800 ......... ............... 210 ( 238) 618...............+ 1140c0000 oo....... ............... 238 ( 618) 677...............+ 228080000 ......... ............... 618 ( 677) 734...............

+ * 450000000 * .o....... .......... 654 677 ( 734) 791 812..........

- * 00020c020 ......... .......... 98 184 ( 117) 233...............= 001508051 ..oo...oo ............... 117 ( 233) 255...............+ 002a000a2 * ......... ............... 233 ( 255) 273 424..........

= 004030000 ....o.... ............... 588 ( 257) 353...............+ 009060100 ..o...o.. ............... 257 ( 353) 240...............

- * 441014400 * ..o.o.... .......... 694 699 ( 726) 781 789..........

- 882038800 ....o.... ............... 726 ( 781) 262...............= 004060000 ......... ............... 781 ( 262) 332...............+ 0080c1100 .....oo.. ............... 262 ( 332) 74...............

- 08a000000 ......... ............... 533 ( 583) 266...............= 004110000 ...oo.... ............... 583 ( 266) 335...............+ 008220000 * ......... ............... 266 ( 335) 143 152..........

- * 441004410 ..o....o. .......... 694 699 ( 720) 777...............- 882008820 ......... ............... 720 ( 777) 281...............= 005100051 ..oo...oo ............... 777 ( 281) 360...............+ 00a2000a2 * ......... ............... 281 ( 360) 273 424..........

= * 005400000 ..o...... .......... 245 546 ( 301) 378...............+ 00a800000 ......... ............... 301 ( 378) 596...............+ 114000000 oo....... ............... 378 ( 596) 654...............

+ * 228000000 ......... .......... 596 626 ( 654) 734...............

- 883028800 ..o...... ............... 726 ( 789) 323...............= 006040000 ......... ............... 789 ( 323) 626...............+ 11c080000 oo....... ............... 323 ( 626) 654...............

= * 014400144 .o....o.. .......... 255 360 ( 424) 472...............+ 028800288 ......... ............... 424 ( 472) 637...............+ 150001500 oo...oo.. ............... 472 ( 637) 694...............

86

+ 2a0002a00 * ......... ............... 637 ( 694) 720 726..........

- * 0020c0200 ......... .......... 216 353 ( 240) 446...............= 015080510 .oo...oo. ............... 240 ( 446) 489...............+ 02a000a20 ......... ............... 446 ( 489) 527...............+ 044101440 * ...o.o... ............... 489 ( 527) 575 581..........

= 040300000 ...o..... ............... 812 ( 495) 593...............+ 090601000 .o...o... ............... 495 ( 593) 450...............

- 8a0000000 ......... ............... 734 ( 791) 500...............= 041100000 ..oo..... ............... 791 ( 500) 546...............+ 082200000 * ......... ............... 500 ( 546) 275 301..........

- * 020c02000 ......... .......... 402 593 ( 450) 650...............= 150805100 oo...oo.. ............... 450 ( 650) 699...............+ 2a000a200 * ......... ............... 650 ( 699) 720 726..........



- 000883040 * .....o... ............... 142 ( 178) 27 97..........

= 000006090 .......o. ............... 178 ( 27) 105...............

+ * 00011c020 ...oo.... .......... 27 163 ( 105) 121...............

- * 0004410a8 2 .....o... .......... 125 191 ( 142) 176 177 178.....

- 000882140 ......o.. ............... 142 ( 177) 42...............= 000014280 ....o.... ............... 177 ( 42) 49...............+ 000028411 .......oo ............... 42 ( 49) 109...............

- 000040388 ......o.. ............... 180 ( 56) 79...............- 000090600 ....o.... ............... 56 ( 79) 47...............= 000020c11 .......oo ............... 79 ( 47) 109...............

= 000041288 .....o... ............... 180 ( 59) 75...............+ 000082410 .......o. ............... 59 ( 75) 104...............+ 000114820 ...oo.... ............... 75 ( 104) 121...............

+ 2 000228051 * .......oo ..... 103 104 105 ( 121) 144 154..........

= 000050288 2 ....o.... ............... 180 ( 62) 80 81 85.....

- 008820500 * ......o.. ............... 274 ( 343) 63 219..........

= 000050a00 ....o.... ............... 343 ( 63) 80...............

+ 2 0000a0411 .......oo ..... 62 63 90 ( 80) 109...............

87

- 008830400 * ....o.... ............... 274 ( 347) 68 215..........

= 000060900 ......o.. ............... 347 ( 68) 222...............

+ * 0011c0200 ..oo..... .......... 68 325 ( 222) 246...............

= 0000a0500 ......o.. ............... 62 ( 81) 219...............

+ * 001140a00 ..oo..... .......... 81 343 ( 219) 246...............

= 0000b0400 ....o.... ............... 62 ( 85) 215...............

+ * 001060800 * ..o...... .......... 85 347 ( 215) 243 244..........

- * 008060100 * ......o.. .......... 261 265 ( 325) 90 222..........

= 0000d0200 ....o.... ............... 325 ( 90) 80...............

= 000106080 2 ...o..... ............... 178 ( 97) 118 119 130.....

- 000882050 .......o. ............... 142 ( 176) 103...............= 0001140a0 ...oo.... ............... 176 ( 103) 121...............

- * 004410a80 2 ....o.... .......... 256 366 ( 274) 343 344 347.....

- 008821400 .....o... ............... 274 ( 344) 106...............= 000142800 ...o..... ............... 344 ( 106) 122...............+ 000284110 ......oo. ............... 106 ( 122) 234...............

= * 00020c110 ......oo. .......... 97 183 ( 118) 234...............

= 00020d000 .....o... ............... 97 ( 119) 408...............

+ 2 01140a000 .oo...... ..... 119 188 577 ( 408) 459...............

- 2 000150822 ...oo.... ..... 47 49 80 ( 109) 125...............= 0002a0054 * .......o. ............... 109 ( 125) 142 228..........

= 00030c000 ...o..... ............... 97 ( 130) 401...............

+ 2 010608000 .o....... ..... 130 200 582 ( 401) 453...............

= 000403880 * .....o... ............... 351 ( 134) 163 183..........

- 088205000 2 .....o... ............... 532 ( 577) 138 146 408.....

= 00040b000 .....o... ............... 577 ( 138) 163...............

+ 2 000806010 .......o. ..... 134 138 202 ( 163) 105...............

88

= 000412880 ....o.... ............... 351 ( 140) 173...............+ 000824100 ......o.. ............... 140 ( 173) 221...............+ 001148200 ..oo..... ............... 173 ( 221) 246...............

+ 2 002280510 * ......oo. ..... 219 221 222 ( 246) 277 311..........

= * 0004500a2 ....o.... .......... 121 336 ( 144) 180...............+ 0008a0144 2 ......o.. ............... 144 ( 180) 56 59 62.....

= 00050a000 ...o..... ............... 577 ( 146) 187...............

+ 2 000a04110 ......oo. ..... 145 146 207 ( 187) 234...............

- * 02a004500 ......o.. .......... 443 448 ( 493) 531...............- 044108a00 ...o..... ............... 493 ( 531) 572...............- 088200411 .......oo ............... 531 ( 572) 150...............= 000510822 ...oo.... ............... 572 ( 150) 191...............+ 000a20054 * .......o. ............... 150 ( 191) 142 228..........

= * 0005400a2 ...o..... .......... 121 336 ( 154) 197...............+ 000a80144 ......o.. ............... 154 ( 197) 405...............+ 011400288 .oo...... ............... 197 ( 405) 456...............+ 022801500 .....oo.. ............... 405 ( 456) 537...............+ 045002a00 * ..o...... ............... 456 ( 537) 585 591..........

- 088304000 * ...o..... ............... 532 ( 582) 159 401..........

= 000609000 .....o... ............... 582 ( 159) 413...............

+ * 011c02000 .oo...... .......... 159 542 ( 413) 459...............

= 000906000 ...o..... ............... 134 ( 183) 118...............

- 000502880 2 ...o..... ............... 351 ( 145) 187 188 200.....

= 000a05000 .....o... ............... 145 ( 188) 408...............

= 000b04000 ...o..... ............... 145 ( 200) 401...............

- 080601000 2 .....o... ............... 499 ( 542) 202 207 413.....

= 000c03000 .....o... ............... 542 ( 202) 163...............

= 000d02000 ...o..... ............... 542 ( 207) 187...............

- 088214000 ....o.... ............... 532 ( 579) 225...............= 001428000 ..o...... ............... 579 ( 225) 248...............+ 002841100 .....oo.. ............... 225 ( 248) 448...............

+ 2 015082200 * .oo...... ..... 243 248 355 ( 448) 493 494..........

89

= * 0014400a8 ..o...... .......... 125 191 ( 228) 252...............+ 002881140 .....oo.. ............... 228 ( 252) 443...............+ 015002280 * .oo...... ............... 252 ( 443) 493 494..........

= * 0020c1100 .....oo.. .......... 215 352 ( 243) 448...............

= 0020d0000 ....o.... ............... 215 ( 244) 617...............

+ 2 1140a0000 oo....... ..... 244 356 783 ( 617) 676...............

- 2 001508220 ..oo..... ..... 118 122 187 ( 234) 256...............= 002a00540 * ......o.. ............... 234 ( 256) 274 429..........

- * 08a014400 2 ....o.... .......... 537 540 ( 591) 261 271 278.....

= 004038800 * ....o.... ............... 591 ( 261) 325 352..........

- 882050000 2 ....o.... ............... 732 ( 783) 265 279 617.....

= 0040b0000 ....o.... ............... 783 ( 265) 325...............

- * 08a004410 .......o. .......... 537 540 ( 585) 269...............= 004118820 ...oo.... ............... 585 ( 269) 336...............+ 008220051 * .......oo ............... 269 ( 336) 144 154..........

= 004128800 ...o..... ............... 591 ( 271) 340...............+ 008241000 .....o... ............... 271 ( 340) 412...............+ 011482000 .oo...... ............... 340 ( 412) 459...............

= * 004500a20 ...o..... .......... 246 554 ( 277) 351...............+ 008a01440 2 .....o... ............... 277 ( 351) 134 140 145.....

= 005028800 * ..o...... ............... 591 ( 278) 355 356..........

= 0050a0000 ..o...... ............... 783 ( 279) 355...............

+ * 00a041100 .....oo.. .......... 278 279 ( 355) 448...............

- * 2a0045000 .....o... .......... 646 653 ( 704) 731...............- 44108a000 ..o...... ............... 704 ( 731) 774...............- 882004110 ......oo. ............... 731 ( 774) 297...............= 005108220 ..oo..... ............... 774 ( 297) 366...............+ 00a200540 * ......o.. ............... 297 ( 366) 274 429..........

= * 005400a20 ..o...... .......... 246 554 ( 311) 390...............+ 00a801440 .....o... ............... 311 ( 390) 609...............+ 114002880 oo....... ............... 390 ( 609) 672...............+ 228015000 ....oo... ............... 609 ( 672) 754...............+ 45002a000 * .o....... ............... 672 ( 754) 809 816..........

- 883040000 ..o...... ............... 732 ( 790) 324...............

90

= 006090000 ....o.... ............... 790 ( 324) 624...............+ 11c020000 oo....... ............... 324 ( 624) 676...............

= 009060000 ..o...... ............... 261 ( 352) 243...............

= 00a050000 ....o.... ............... 278 ( 356) 617...............

- 882140000 ...o..... ............... 732 ( 785) 417...............= 014280000 .o....... ............... 785 ( 417) 465...............+ 028411000 ....oo... ............... 417 ( 465) 653...............

+ 2 150822000 * oo....... ..... 453 465 595 ( 653) 704 705..........

= * 014400a80 .o....... .......... 256 366 ( 429) 485...............+ 028811400 ....oo... ............... 429 ( 485) 646...............+ 150022800 * oo....... ............... 485 ( 646) 704 705..........

= * 020c11000 ....oo... .......... 401 592 ( 453) 653...............

= * 02a005400 .....o... .......... 443 448 ( 494) 532...............+ 04410a800 2 ...o..... ............... 494 ( 532) 577 579 582.....

- * 8a0144000 2 ...o..... .......... 754 758 ( 816) 499 522 541.....

= 040388000 * ...o..... ............... 816 ( 499) 542 592..........

- * 8a0044100 ......o.. .......... 754 758 ( 809) 519...............= 041188200 ..oo..... ............... 809 ( 519) 554...............+ 082200510 * ......oo. ............... 519 ( 554) 277 311..........

= 041288000 ..o...... ............... 816 ( 522) 567...............+ 082410000 ....o.... ............... 522 ( 567) 622...............+ 114820000 oo....... ............... 567 ( 622) 676...............

- 2 022805100 .....oo.. ..... 408 412 413 ( 459) 540...............= 04500a200 * ..o...... ............... 459 ( 540) 585 591..........

= 050288000 .o....... ............... 816 ( 541) 595...............+ 0a0411000 ....oo... ............... 541 ( 595) 653...............

= 090600000 .o....... ............... 499 ( 592) 453...............

= * 2a0054000 ....o.... .......... 646 653 ( 705) 732...............+ 4410a8000 2 ..o...... ............... 705 ( 732) 783 785 790.....

- 2 228051000 ....oo... ..... 617 622 624 ( 676) 758...............= 4500a2000 * .o....... ............... 676 ( 758) 809 816..........



91

- 000510051 ...oo..oo ............... 578 ( 148) 192...............- 000a200a2 ......... ............... 148 ( 192) 229...............- 001440144 ..o...o.. ............... 192 ( 229) 251...............- 002880288 ......... ............... 229 ( 251) 442...............- 015001500 .oo..oo.. ............... 251 ( 442) 491...............- 02a002a00 ......... ............... 442 ( 491) 529...............- 044104410 ...o...o. ............... 491 ( 529) 578...............- 088208820 ......... ............... 529 ( 578) 148...............= 000510051 ...oo..oo ............... 578 ( 148) 192...............


prospective tiles: 177- 0005100a2 ...oo.... ............... 571 ( 149) 193...............- 000a20144 ......o.. ............... 149 ( 193) 230...............- 001440288 ..o...... ............... 193 ( 230) 253...............- 002881500 .....oo.. ............... 230 ( 253) 444...............- 015002a00 .oo...... ............... 253 ( 444) 492...............- 02a004410 .......o. ............... 444 ( 492) 530...............- 044108820 ...o..... ............... 492 ( 530) 571...............- 088200051 .......oo ............... 530 ( 571) 149...............= 0005100a2 ...oo.... ............... 571 ( 149) 193...............


prospective tiles: 178- 000518820 ...oo.... ............... 576 ( 151) 190...............- 000a20051 .......oo ............... 151 ( 190) 227...............- 0014400a2 ..o...... ............... 190 ( 227) 250...............- 002880144 ......o.. ............... 227 ( 250) 441...............- 015000288 .oo...... ............... 250 ( 441) 490...............- 02a001500 .....oo.. ............... 441 ( 490) 528...............- 044102a00 ...o..... ............... 490 ( 528) 576...............- 088204410 .......o. ............... 528 ( 576) 151...............= 000518820 ...oo.... ............... 576 ( 151) 190...............


prospective tiles: 179- 000540054 ...o...o. ............... 339 ( 153) 196...............- 000a800a8 ......... ............... 153 ( 196) 406...............- 011401140 .oo..oo.. ............... 196 ( 406) 457...............- 022802280 ......... ............... 406 ( 457) 538...............- 045004500 ..o...o.. ............... 457 ( 538) 587...............- 08a008a00 ......... ............... 538 ( 587) 267...............- 004110411 ...oo..oo ............... 587 ( 267) 339...............- 008220822 ......... ............... 267 ( 339) 153...............= 000540054 ...o...o. ............... 339 ( 153) 196...............


92

prospective tiles: 180- 0005400a8 ...o..... ............... 337 ( 155) 198...............- 000a81140 .....oo.. ............... 155 ( 198) 407...............- 011402280 .oo...... ............... 198 ( 407) 458...............- 022804500 ......o.. ............... 407 ( 458) 539...............- 045008a00 ..o...... ............... 458 ( 539) 584...............- 08a000411 .......oo ............... 539 ( 584) 268...............- 004110822 ...oo.... ............... 584 ( 268) 337...............- 008220054 .......o. ............... 268 ( 337) 155...............= 0005400a8 ...o..... ............... 337 ( 155) 198...............


prospective tiles: 181- 000540822 ...o..... ............... 338 ( 156) 195...............- 000a80054 .......o. ............... 156 ( 195) 404...............- 0114000a8 .oo...... ............... 195 ( 404) 455...............- 022801140 .....oo.. ............... 404 ( 455) 536...............- 045002280 ..o...... ............... 455 ( 536) 586...............- 08a004500 ......o.. ............... 536 ( 586) 270...............- 004118a00 ...oo.... ............... 586 ( 270) 338...............- 008220411 .......oo ............... 270 ( 338) 156...............= 000540822 ...o..... ............... 338 ( 156) 195...............


prospective tiles: 182- 005100054 ..oo...o. ............... 769 ( 282) 361...............- 00a2000a8 ......... ............... 282 ( 361) 430...............- 014401140 .o...oo.. ............... 361 ( 430) 478...............- 028802280 ......... ............... 430 ( 478) 642...............- 150004500 oo....o.. ............... 478 ( 642) 698...............- 2a0008a00 ......... ............... 642 ( 698) 714...............- 441000411 ..o....oo ............... 698 ( 714) 769...............- 882000822 ......... ............... 714 ( 769) 282...............= 005100054 ..oo...o. ............... 769 ( 282) 361...............



= 0051000a2 ..oo..... ............... 761 ( 283) 362...............+ 00a200144 ......o.. ............... 283 ( 362) 425...............+ 014400288 .o....... ............... 362 ( 425) 477...............+ 028801500 .....oo.. ............... 425 ( 477) 640...............+ 150002a00 oo....... ............... 477 ( 640) 695...............

- 2a0001500 .....oo.. ............... 633 ( 692) 719...............- 441002a00 ..o...... ............... 692 ( 719) 775...............- 882004410 .......o. ............... 719 ( 775) 298...............= 005108820 ..oo..... ............... 775 ( 298) 358...............

93

+ 00a200051 .......oo ............... 298 ( 358) 422...............

= 0141100a2 .o.oo.... ............... 761 ( 416) 463...............+ 028220144 ......o.. ............... 416 ( 463) 648...............+ 150541288 oo.o.o... ............... 463 ( 648) 706...............+ 2a0a82410 .......o. ............... 648 ( 706) 733...............+ 441504820 ..oo..... ............... 706 ( 733) 787...............+ 882a08051 .......oo ............... 733 ( 787) 422...............

- 2a0011410 ....oo.o. ............... 633 ( 700) 727...............- 441022820 ..o...... ............... 700 ( 727) 786...............- 882145051 ...o.o.oo ............... 727 ( 786) 418...............= 01428a0a2 .o....... ............... 786 ( 418) 464...............+ 028405144 .....oo.. ............... 418 ( 464) 652...............+ 15080a288 oo....... ............... 464 ( 652) 695...............

- * 0144000a2 .o....... .......... 358 787 ( 422) 471...............= 028800144 ......o.. ............... 422 ( 471) 633...............+ 150000288 * oo....... ............... 471 ( 633) 692 700..........

- * 2a0004410 .......o. .......... 640 652 ( 695) 722...............= 441008820 ..o...... ............... 695 ( 722) 761...............+ 882000051 * .......oo ............... 722 ( 761) 283 416..........


prospective tiles: 189- 0051000a8 ..oo..... ............... 762 ( 284) 369...............- 00a201140 .....oo.. ............... 284 ( 369) 433...............- 014402280 .o....... ............... 369 ( 433) 482...............- 028804500 ......o.. ............... 433 ( 482) 644...............- 150008a00 oo....... ............... 482 ( 644) 688...............- 2a0000411 .......oo ............... 644 ( 688) 715...............- 441000822 ..o...... ............... 688 ( 715) 762...............- 882000054 .......o. ............... 715 ( 762) 284...............= 0051000a8 ..oo..... ............... 762 ( 284) 369...............


prospective tiles: 190- 005100144 ..oo..o.. ............... 763 ( 285) 363...............- 00a200288 ......... ............... 285 ( 363) 432...............- 014401500 .o...oo.. ............... 363 ( 432) 480...............- 028802a00 ......... ............... 432 ( 480) 641...............- 150004410 oo.....o. ............... 480 ( 641) 697...............- 2a0008820 ......... ............... 641 ( 697) 708...............- 441000051 ..o....oo ............... 697 ( 708) 763...............- 8820000a2 ......... ............... 708 ( 763) 285...............= 005100144 ..oo..o.. ............... 763 ( 285) 363...............


94

prospective tiles: 191- 005100288 ..oo..... ............... 765 ( 286) 371...............- 00a201500 .....oo.. ............... 286 ( 371) 435...............- 014402a00 .o....... ............... 371 ( 435) 481...............- 028804410 .......o. ............... 435 ( 481) 643...............- 150008820 oo....... ............... 481 ( 643) 682...............- 2a0000051 .......oo ............... 643 ( 682) 710...............- 4410000a2 ..o...... ............... 682 ( 710) 765...............- 882000144 ......o.. ............... 710 ( 765) 286...............= 005100288 ..oo..... ............... 765 ( 286) 371...............


prospective tiles: 192- 005100411 ..oo...oo ............... 778 ( 287) 367...............- 00a200822 ......... ............... 287 ( 367) 421...............- 014400054 .o.....o. ............... 367 ( 421) 470...............- 0288000a8 ......... ............... 421 ( 470) 636...............- 150001140 oo...oo.. ............... 470 ( 636) 693...............- 2a0002280 ......... ............... 636 ( 693) 721...............- 441004500 ..o...o.. ............... 693 ( 721) 778...............- 882008a00 ......... ............... 721 ( 778) 287...............= 005100411 ..oo...oo ............... 778 ( 287) 367...............


prospective tiles: 193- 005100510 ..oo..oo. ............... 784 ( 288) 368...............- 00a200a20 ......... ............... 288 ( 368) 431...............- 014401440 .o...o... ............... 368 ( 431) 479...............- 028802880 ......... ............... 431 ( 479) 645...............- 150015000 oo..oo... ............... 479 ( 645) 702...............- 2a002a000 ......... ............... 645 ( 702) 729...............- 441044100 ..o...o.. ............... 702 ( 729) 784...............- 882088200 ......... ............... 729 ( 784) 288...............= 005100510 ..oo..oo. ............... 784 ( 288) 368...............


prospective tiles: 194- 005100822 ..oo..... ............... 767 ( 289) 359...............- 00a200054 .......o. ............... 289 ( 359) 423...............- 0144000a8 .o....... ............... 359 ( 423) 475...............- 028801140 .....oo.. ............... 423 ( 475) 638...............- 150002280 oo....... ............... 475 ( 638) 696...............- 2a0004500 ......o.. ............... 638 ( 696) 723...............- 441008a00 ..o...... ............... 696 ( 723) 767...............- 882000411 .......oo ............... 723 ( 767) 289...............= 005100822 ..oo..... ............... 767 ( 289) 359...............

95


prospective tiles: 195- 005100a20 ..oo..... ............... 768 ( 290) 370...............- 00a201440 .....o... ............... 290 ( 370) 434...............- 014402880 .o....... ............... 370 ( 434) 486...............- 028815000 ....oo... ............... 434 ( 486) 647...............- 15002a000 oo....... ............... 486 ( 647) 703...............- 2a0044100 ......o.. ............... 647 ( 703) 730...............- 441088200 ..o...... ............... 703 ( 730) 768...............- 882000510 ......oo. ............... 730 ( 768) 290...............= 005100a20 ..oo..... ............... 768 ( 290) 370...............


prospective tiles: 196- 005101140 ..oo.oo.. ............... 764 ( 291) 372...............- 00a202280 ......... ............... 291 ( 372) 437...............- 014404500 .o....o.. ............... 372 ( 437) 484...............- 028808a00 ......... ............... 437 ( 484) 634...............- 150000411 oo.....oo ............... 484 ( 634) 690...............- 2a0000822 ......... ............... 634 ( 690) 709...............- 441000054 ..o....o. ............... 690 ( 709) 764...............- 8820000a8 ......... ............... 709 ( 764) 291...............= 005101140 ..oo.oo.. ............... 764 ( 291) 372...............


prospective tiles: 197- 005101500 ..oo.oo.. ............... 766 ( 292) 373...............- 00a202a00 ......... ............... 292 ( 373) 436...............- 014404410 .o.....o. ............... 373 ( 436) 483...............- 028808820 ......... ............... 436 ( 483) 628...............- 150000051 oo.....oo ............... 483 ( 628) 684...............- 2a00000a2 ......... ............... 628 ( 684) 712...............- 441000144 ..o...o.. ............... 684 ( 712) 766...............- 882000288 ......... ............... 712 ( 766) 292...............= 005101500 ..oo.oo.. ............... 766 ( 292) 373...............


prospective tiles: 198- 005102280 ..oo..... ............... 770 ( 293) 375...............- 00a204500 ......o.. ............... 293 ( 375) 439...............- 014408a00 .o....... ............... 375 ( 439) 473...............- 028800411 .......oo ............... 439 ( 473) 635...............- 150000822 oo....... ............... 473 ( 635) 683...............- 2a0000054 .......o. ............... 635 ( 683) 711...............- 4410000a8 ..o...... ............... 683 ( 711) 770...............- 882001140 .....oo.. ............... 711 ( 770) 293...............= 005102280 ..oo..... ............... 770 ( 293) 375...............

96


prospective tiles: 199- 005102a00 ..oo..... ............... 771 ( 294) 374...............- 00a204410 .......o. ............... 294 ( 374) 438...............- 014408820 .o....... ............... 374 ( 438) 467...............- 028800051 .......oo ............... 438 ( 467) 630...............- 1500000a2 oo....... ............... 467 ( 630) 686...............- 2a0000144 ......o.. ............... 630 ( 686) 713...............- 441000288 ..o...... ............... 686 ( 713) 771...............- 882001500 .....oo.. ............... 713 ( 771) 294...............= 005102a00 ..oo..... ............... 771 ( 294) 374...............


prospective tiles: 200- 005104410 ..oo...o. ............... 773 ( 295) 376...............- 00a208820 ......... ............... 295 ( 376) 420...............- 014400051 .o.....oo ............... 376 ( 420) 469...............- 0288000a2 ......... ............... 420 ( 469) 632...............- 150000144 oo....o.. ............... 469 ( 632) 687...............- 2a0000288 ......... ............... 632 ( 687) 717...............- 441001500 ..o..oo.. ............... 687 ( 717) 773...............- 882002a00 ......... ............... 717 ( 773) 295...............= 005104410 ..oo...o. ............... 773 ( 295) 376...............


prospective tiles: 201- 005104500 ..oo..o.. ............... 772 ( 296) 377...............- 00a208a00 ......... ............... 296 ( 377) 426...............- 014400411 .o.....oo ............... 377 ( 426) 474...............- 028800822 ......... ............... 426 ( 474) 629...............- 150000054 oo.....o. ............... 474 ( 629) 685...............- 2a00000a8 ......... ............... 629 ( 685) 716...............- 441001140 ..o..oo.. ............... 685 ( 716) 772...............- 882002280 ......... ............... 716 ( 772) 296...............= 005104500 ..oo..o.. ............... 772 ( 296) 377...............


prospective tiles: 202- 005108a00 ..oo..... ............... 776 ( 299) 364...............- 00a200411 .......oo ............... 299 ( 364) 427...............- 014400822 .o....... ............... 364 ( 427) 468...............- 028800054 .......o. ............... 427 ( 468) 631...............- 1500000a8 oo....... ............... 468 ( 631) 691...............- 2a0001140 .....oo.. ............... 631 ( 691) 718...............- 441002280 ..o...... ............... 691 ( 718) 776...............- 882004500 ......o.. ............... 718 ( 776) 299...............

97

= 005108a00 ..oo..... ............... 776 ( 299) 364...............


prospective tiles: 203- 005188200 ..oo..... ............... 782 ( 300) 365...............- 00a200510 ......oo. ............... 300 ( 365) 428...............- 014400a20 .o....... ............... 365 ( 428) 476...............- 028801440 .....o... ............... 428 ( 476) 639...............- 150002880 oo....... ............... 476 ( 639) 701...............- 2a0015000 ....oo... ............... 639 ( 701) 728...............- 44102a000 ..o...... ............... 701 ( 728) 782...............- 882044100 ......o.. ............... 728 ( 782) 300...............= 005188200 ..oo..... ............... 782 ( 300) 365...............


prospective tiles: 204- 005400051 ..o....oo ............... 565 ( 302) 381...............- 00a8000a2 ......... ............... 302 ( 381) 601...............- 114000144 oo....o.. ............... 381 ( 601) 660...............- 228000288 ......... ............... 601 ( 660) 745...............- 450001500 .o...oo.. ............... 660 ( 745) 803...............- 8a0002a00 ......... ............... 745 ( 803) 514...............- 041104410 ..oo...o. ............... 803 ( 514) 565...............- 082208820 ......... ............... 514 ( 565) 302...............= 005400051 ..o....oo ............... 565 ( 302) 381...............


prospective tiles: 205- 0054000a2 ..o...... ............... 547 ( 304) 383...............- 00a800144 ......o.. ............... 304 ( 383) 602...............- 114000288 oo....... ............... 383 ( 602) 664...............- 228001500 .....oo.. ............... 602 ( 664) 747...............- 450002a00 .o....... ............... 664 ( 747) 805...............- 8a0004410 .......o. ............... 747 ( 805) 517...............- 041108820 ..oo..... ............... 805 ( 517) 547...............- 082200051 .......oo ............... 517 ( 547) 304...............= 0054000a2 ..o...... ............... 547 ( 304) 383...............



= 0054000a8 ..o...... ............... 548 ( 305) 389...............+ 00a801140 .....oo.. ............... 305 ( 389) 608...............+ 114002280 oo....... ............... 389 ( 608) 668...............+ 228004500 ......o.. ............... 608 ( 668) 752...............+ 450008a00 .o....... ............... 668 ( 752) 798...............

98

- 8a0004500 ......o.. ............... 746 ( 806) 518...............- 041108a00 ..oo..... ............... 806 ( 518) 553...............- 082200411 .......oo ............... 518 ( 553) 310...............= 005400822 ..o...... ............... 553 ( 310) 380...............+ 00a800054 .......o. ............... 310 ( 380) 600...............

- * 8a0000411 .......oo .......... 752 756 ( 798) 508...............= 041100822 ..oo..... ............... 798 ( 508) 548...............+ 082200054 * .......o. ............... 508 ( 548) 305 621..........

- 8a0105411 ...o.o.oo ............... 746 ( 814) 521...............= 04120a822 ..o...... ............... 814 ( 521) 568...............+ 082415054 ....oo.o. ............... 521 ( 568) 623...............+ 11482a0a8 oo....... ............... 568 ( 623) 674...............+ 228044140 ......o.. ............... 623 ( 674) 756...............+ 450088280 .o....... ............... 674 ( 756) 798...............

- 1145010a8 oo.o.o... ............... 548 ( 621) 680...............- 228a02140 ......o.. ............... 621 ( 680) 759...............- 450514280 .o.oo.... ............... 680 ( 759) 817...............- 8a0a28411 .......oo ............... 759 ( 817) 523...............= 041440822 ..o...... ............... 817 ( 523) 569...............+ 082880054 .......o. ............... 523 ( 569) 600...............

- * 1140000a8 oo....... .......... 380 569 ( 600) 663...............= 228001140 .....oo.. ............... 600 ( 663) 746...............+ 450002280 * .o....... ............... 663 ( 746) 806 814..........


prospective tiles: 212- 005400144 ..o...o.. ............... 549 ( 306) 384...............- 00a800288 ......... ............... 306 ( 384) 607...............- 114001500 oo...oo.. ............... 384 ( 607) 666...............- 228002a00 ......... ............... 607 ( 666) 748...............- 450004410 .o.....o. ............... 666 ( 748) 807...............- 8a0008820 ......... ............... 748 ( 807) 501...............- 041100051 ..oo...oo ............... 807 ( 501) 549...............- 0822000a2 ......... ............... 501 ( 549) 306...............= 005400144 ..o...o.. ............... 549 ( 306) 384...............


prospective tiles: 213- 005400288 ..o...... ............... 551 ( 307) 391...............- 00a801500 .....oo.. ............... 307 ( 391) 610...............- 114002a00 oo....... ............... 391 ( 610) 667...............- 228004410 .......o. ............... 610 ( 667) 751...............- 450008820 .o....... ............... 667 ( 751) 792...............- 8a0000051 .......oo ............... 751 ( 792) 503...............- 0411000a2 ..oo..... ............... 792 ( 503) 551...............

99

- 082200144 ......o.. ............... 503 ( 551) 307...............= 005400288 ..o...... ............... 551 ( 307) 391...............


prospective tiles: 214- 005400411 ..o....oo ............... 566 ( 308) 387...............- 00a800822 ......... ............... 308 ( 387) 598...............- 114000054 oo.....o. ............... 387 ( 598) 658...............- 2280000a8 ......... ............... 598 ( 658) 744...............- 450001140 .o...oo.. ............... 658 ( 744) 802...............- 8a0002280 ......... ............... 744 ( 802) 515...............- 041104500 ..oo..o.. ............... 802 ( 515) 566...............- 082208a00 ......... ............... 515 ( 566) 308...............= 005400411 ..o....oo ............... 566 ( 308) 387...............


prospective tiles: 215- 005400540 ..o...o.. ............... 564 ( 309) 388...............- 00a800a80 ......... ............... 309 ( 388) 615...............- 114011400 oo..oo... ............... 388 ( 615) 673...............- 228022800 ......... ............... 615 ( 673) 755...............- 450045000 .o...o... ............... 673 ( 755) 811...............- 8a008a000 ......... ............... 755 ( 811) 513...............- 041104110 ..oo..oo. ............... 811 ( 513) 564...............- 082208220 ......... ............... 513 ( 564) 309...............= 005400540 ..o...o.. ............... 564 ( 309) 388...............


prospective tiles: 216- 005400a80 ..o...... ............... 555 ( 312) 398...............- 00a811400 ....oo... ............... 312 ( 398) 616...............- 114022800 oo....... ............... 398 ( 616) 675...............- 228045000 .....o... ............... 616 ( 675) 757...............- 45008a000 .o....... ............... 675 ( 757) 804...............- 8a0004110 ......oo. ............... 757 ( 804) 516...............- 041108220 ..oo..... ............... 804 ( 516) 555...............- 082200540 ......o.. ............... 516 ( 555) 312...............= 005400a80 ..o...... ............... 555 ( 312) 398...............


prospective tiles: 217- 005401140 ..o..oo.. ............... 550 ( 313) 392...............- 00a802280 ......... ............... 313 ( 392) 612...............- 114004500 oo....o.. ............... 392 ( 612) 670...............- 228008a00 ......... ............... 612 ( 670) 741...............- 450000411 .o.....oo ............... 670 ( 741) 799...............- 8a0000822 ......... ............... 741 ( 799) 502...............

100

- 041100054 ..oo...o. ............... 799 ( 502) 550...............- 0822000a8 ......... ............... 502 ( 550) 313...............= 005401140 ..o..oo.. ............... 550 ( 313) 392...............


prospective tiles: 218- 005401500 ..o..oo.. ............... 552 ( 314) 393...............- 00a802a00 ......... ............... 314 ( 393) 611...............- 114004410 oo.....o. ............... 393 ( 611) 669...............- 228008820 ......... ............... 611 ( 669) 735...............- 450000051 .o.....oo ............... 669 ( 735) 794...............- 8a00000a2 ......... ............... 735 ( 794) 505...............- 041100144 ..oo..o.. ............... 794 ( 505) 552...............- 082200288 ......... ............... 505 ( 552) 314...............= 005401500 ..o..oo.. ............... 552 ( 314) 393...............


prospective tiles: 219- 005402280 ..o...... ............... 557 ( 315) 395...............- 00a804500 ......o.. ............... 315 ( 395) 614...............- 114008a00 oo....... ............... 395 ( 614) 661...............- 228000411 .......oo ............... 614 ( 661) 742...............- 450000822 .o....... ............... 661 ( 742) 793...............- 8a0000054 .......o. ............... 742 ( 793) 504...............- 0411000a8 ..oo..... ............... 793 ( 504) 557...............- 082201140 .....oo.. ............... 504 ( 557) 315...............= 005402280 ..o...... ............... 557 ( 315) 395...............


prospective tiles: 220- 005402a00 ..o...... ............... 558 ( 316) 394...............- 00a804410 .......o. ............... 316 ( 394) 613...............- 114008820 oo....... ............... 394 ( 613) 655...............- 228000051 .......oo ............... 613 ( 655) 737...............- 4500000a2 .o....... ............... 655 ( 737) 796...............- 8a0000144 ......o.. ............... 737 ( 796) 506...............- 041100288 ..oo..... ............... 796 ( 506) 558...............- 082201500 .....oo.. ............... 506 ( 558) 316...............= 005402a00 ..o...... ............... 558 ( 316) 394...............


prospective tiles: 221- 005404410 ..o....o. ............... 560 ( 317) 396...............- 00a808820 ......... ............... 317 ( 396) 597...............- 114000051 oo.....oo ............... 396 ( 597) 657...............- 2280000a2 ......... ............... 597 ( 657) 739...............- 450000144 .o....o.. ............... 657 ( 739) 797...............

101

- 8a0000288 ......... ............... 739 ( 797) 510...............- 041101500 ..oo.oo.. ............... 797 ( 510) 560...............- 082202a00 ......... ............... 510 ( 560) 317...............= 005404410 ..o....o. ............... 560 ( 317) 396...............


prospective tiles: 222- 005404500 ..o...o.. ............... 559 ( 318) 397...............- 00a808a00 ......... ............... 318 ( 397) 603...............- 114000411 oo.....oo ............... 397 ( 603) 662...............- 228000822 ......... ............... 603 ( 662) 736...............- 450000054 .o.....o. ............... 662 ( 736) 795...............- 8a00000a8 ......... ............... 736 ( 795) 509...............- 041101140 ..oo.oo.. ............... 795 ( 509) 559...............- 082202280 ......... ............... 509 ( 559) 318...............= 005404500 ..o...o.. ............... 559 ( 318) 397...............


prospective tiles: 223- 005408220 ..o...... ............... 561 ( 319) 386...............- 00a800540 ......o.. ............... 319 ( 386) 605...............- 114000a80 oo....... ............... 386 ( 605) 671...............- 228011400 ....oo... ............... 605 ( 671) 753...............- 450022800 .o....... ............... 671 ( 753) 810...............- 8a0045000 .....o... ............... 753 ( 810) 520...............- 04118a000 ..oo..... ............... 810 ( 520) 561...............- 082204110 ......oo. ............... 520 ( 561) 319...............= 005408220 ..o...... ............... 561 ( 319) 386...............


prospective tiles: 224- 005408820 ..o...... ............... 562 ( 320) 379...............- 00a800051 .......oo ............... 320 ( 379) 599...............- 1140000a2 oo....... ............... 379 ( 599) 659...............- 228000144 ......o.. ............... 599 ( 659) 740...............- 450000288 .o....... ............... 659 ( 740) 801...............- 8a0001500 .....oo.. ............... 740 ( 801) 512...............- 041102a00 ..oo..... ............... 801 ( 512) 562...............- 082204410 .......o. ............... 512 ( 562) 320...............= 005408820 ..o...... ............... 562 ( 320) 379...............


prospective tiles: 225- 005408a00 ..o...... ............... 563 ( 321) 385...............- 00a800411 .......oo ............... 321 ( 385) 604...............- 114000822 oo....... ............... 385 ( 604) 656...............- 228000054 .......o. ............... 604 ( 656) 738...............

102

- 4500000a8 .o....... ............... 656 ( 738) 800...............- 8a0001140 .....oo.. ............... 738 ( 800) 511...............- 041102280 ..oo..... ............... 800 ( 511) 563...............- 082204500 ......o.. ............... 511 ( 563) 321...............= 005408a00 ..o...... ............... 563 ( 321) 385...............



103

Width 9 - z.dat Zero linkage list

= 3 000000000 3 ......... 0 28 69 160 ( 0) 0 13 37 92

= 3 000001000 .....o... 0 28 69 160 ( 13) 94...............

+ 3 000103000 ...o.o... 13 33 73 161 ( 94) 114...............

- 00080c000 3 ......... ............... 137 ( 166) 28 33 45 99

= 000008000 3 ......... ............... 166 ( 28) 0 13 37 92

= 000009000 .....o... ............... 166 ( 33) 94...............

= 3 000010000 * ....o.... 0 28 69 160 ( 37) 52 209..........

= 000018000 * ....o.... ............... 166 ( 45) 52 209..........

= 3 000030100 ....o.o.. 37 45 78 170 ( 52) 213...............

- 00081c000 * ....o.... ............... 137 ( 171) 55 211..........

= 000038100 ....o.o.. ............... 171 ( 55) 213...............

= * 000080000 3 ......... .......... 88 329 ( 69) 0 13 37 92

= * 000081000 .....o... .......... 88 329 ( 73) 94...............

= * 000090000 * ....o.... .......... 88 329 ( 78) 52 209..........

= * 0000b0100 ....o.o.. .......... 91 333 ( 84) 213...............

= 0000c0800 3 ......... ............... 327 ( 88) 69 73 78 110

= 0000c1800 .....o... ............... 327 ( 89) 111...............

+ * 000183000 ...o.o... .......... 89 331 ( 111) 114...............

= 0000d0800 * ....o.... ............... 327 ( 91) 84 217..........

= 3 000100000 ...o..... 0 28 69 160 ( 92) 126...............

+ 3 000301000 ...o.o... 92 99 110 181 ( 126) 399...............

= 000108000 ...o..... ............... 166 ( 99) 126...............

- 00080d000 .....o... ............... 137 ( 169) 101...............= 00010b000 ...o.o... ............... 169 ( 101) 114...............

= * 000180000 ...o..... .......... 88 329 ( 110) 126...............

104

= 0001c0800 ...o..... ............... 327 ( 112) 131...............

+ * 000381000 ...o.o... .......... 112 334 ( 131) 399...............

- 00090c000 ...o..... ............... 137 ( 186) 129...............= 000309000 ...o.o... ............... 186 ( 129) 399...............

- 000c08000 3 ......... ............... 544 ( 204) 160 161 170 181

= 000800000 3 ......... ............... 204 ( 160) 0 13 37 92

= 000801000 .....o... ............... 204 ( 161) 94...............

= 000810000 * ....o.... ............... 204 ( 170) 52 209..........

- 000c18000 * ....o.... ............... 544 ( 206) 174 235..........

= 000830100 ....o.o.. ............... 206 ( 174) 213...............

= 000900000 ...o..... ............... 204 ( 181) 126...............

- 000c09000 .....o... ............... 544 ( 205) 182...............= 000903000 ...o.o... ............... 205 ( 182) 114...............

- 000d08000 ...o..... ............... 544 ( 208) 199...............= 000b01000 ...o.o... ............... 208 ( 199) 399...............

= 3 001030000 ..o.o.... 37 45 78 170 ( 209) 237...............

= 001038000 ..o.o.... ............... 171 ( 211) 237...............

= * 0010b0000 ..o.o.... .......... 91 333 ( 217) 237...............

= 001830000 ..o.o.... ............... 206 ( 235) 237...............

- 3 001060200 ..o...... 52 55 84 174 ( 213) 241...............= 0020c0411 .......oo ............... 213 ( 241) 447...............+ 015080822 .oo...... ............... 241 ( 447) 488...............+ 02a000054 .......o. ............... 447 ( 488) 526...............+ 0441010a8 ...o.o... ............... 488 ( 526) 574...............+ 088203040 .....o... ............... 526 ( 574) 137...............+ 000406080 3 ......... ............... 574 ( 137) 166 169 171 186

- 3 000206010 .......o. 94 101 111 182 ( 114) 410...............- 01140c020 .oo...... ............... 114 ( 410) 461...............- 022808051 .......oo ............... 410 ( 461) 534...............- 0450000a2 ..o...... ............... 461 ( 534) 589...............- 08a010144 ....o.o.. ............... 534 ( 589) 259...............= 004030288 ....o.... ............... 589 ( 259) 327...............+ 008060400 3 ......... ............... 259 ( 327) 88 89 91 112

105

- 3 010602000 .o....... 126 129 131 199 ( 399) 451...............- 020c04110 ......oo. ............... 399 ( 451) 651...............- 150808220 oo....... ............... 451 ( 651) 689...............- 2a0000540 ......o.. ............... 651 ( 689) 725...............- 441010a80 ..o.o.... ............... 689 ( 725) 780...............- 882030400 ....o.... ............... 725 ( 780) 264...............= 004060800 3 ......... ............... 780 ( 264) 329 331 333 334

= 0080c0000 3 ......... ............... 264 ( 329) 69 73 78 110

= 0080c1000 .....o... ............... 264 ( 331) 111...............

= 0080d0000 * ....o.... ............... 264 ( 333) 84 217..........

= 0081c0000 ...o..... ............... 264 ( 334) 131...............

- 3 002060100 ......o.. 209 211 217 235 ( 237) 619...............- 1140c0200 oo....... ............... 237 ( 619) 678...............- 228080510 ......oo. ............... 619 ( 678) 743...............- 450000a20 .o....... ............... 678 ( 743) 813...............- 8a0101440 ...o.o... ............... 743 ( 813) 497...............= 040302880 ...o..... ............... 813 ( 497) 544...............+ 080604000 3 ......... ............... 497 ( 544) 204 205 206 208


106

10 WIDTH 10

Width 10

roman titles

pg10 - zero component tiles

pgg10 - zero component central avatar

pggg10 - zero component left avatar

ph10 - zero component samples

pi10 - some isolated cycle samples

pj10 - sample with 4 nodes

pj10a - variant samplle with 4 nodes

pk10 - sample with 6 nodes

pl10 - another sample

pm10 - sample with 3 nodes

pn10 - cycles (not length 8)

po10 - additional 3-node samples

pp10 - sample with 7 nodes

pq10 - sample with 3 nodes

ps10 - G’ph of zero component

z.dat - linkage list of zero component

greek titles

bet10a - bet10d beta component

gam10a - gam10n gamma component

1845 nodes

2187 links

98 components

maximum linkage: 5


zero: 97

alpha: 70

beta: 70

gamma: 204

8 3-nodes: 24

2 4-nodes: 8

4 6-nodes: 24

4 7-nodes: 28

2 6-cycles: 2

63 8-cycles: 63

2 10-cycles: 2

4 18-cycles: 4

(93?) ...

107



zero component

97 nodes

469252

0

530

1829

891

1569

219

632

115

643

13

94

167

28

33

37

45

52

173

55

69

73

78

91

84

88

89

112

170

92161

183

211

273

245

454

753

280

370

458

528

394

461

752

474

746

354

110 127

373

132

171

210

201

206

208 248

215

369

225

365

99

113

188

130

162

176

184

207

212 217

223 226

278 138

246 742

249355

356

456

357

367

455

381

395

399465

747750

1568 698

943 1805

466

462

108




13

37 92

211

94

115

273

891

52

215

219

127

462

530

1569

365

367

369

373

399

112 84

225

132

466

278

469252206

207

208

210

249

176

248

201

474 280

184

632943

161

162

171

183

245

69

73

78

110

223

18051829 643

1568

central avatar

698 right avatarleft avatar

89

112

0

109


December 17, 1996pggg10.draw


115

891 219

530

1569

367

112

84

466

278249

176

474

280

184

632943

18051829

698

643

1568

left avatar

88

89

91

113

226454

455

456

458

461 84

225 69

73

78

110223

132278112

354355356370394

01337922119452

215

462 127

381

528

357

395

115

891

252

469

530

219

273

110


ph10.draw February 15, 1994

zero component943

1568

632

167

943

1568

632

167

469

399278891

1568

469

399278891

1568

188130

632

188130

632

000

1394115

698

1805

698

1829

458528530

1805

643

226278891

1569

750248252

206161000

111


pi10.draw February 23, 1994

isolated cycles

694 694

488 488

458

458

458

458

112


pj10.drawApril 23, 1994

4 nodes

1154

696

11541272

696

642

1272

642

1272

1272

1154

696

11541272

642

1070

1149

952

1448

1070 952

1449

1448

1272

1272

1154

696

11541272

642

113


pj10a.draw April 23, 1994

4 nodes

1154

1272

1272

1154

696

11541272

642

952

6421272

6961272

10701149

14481070

1154

1272

696

642

1272

1070

952

1449

1448

1070

114


pk10.draw April 24, 1994

small components

334

1333

1351

924

902

1341

334

1333

1351

924

982

982

1333

1341

334

1333

1351

924

982

982

1333

1341

1341

1333

1351 924

334

902

115


November 28, 1996pk10.draw

small components

1246

1246

735

735

1175

1175

116


pm10.draw November 30, 1996

635

959

967

959

635

967

635

635

635

967

967

959

959

3 nodes647

716

717

647

716

717

647

716

phase alternate

117


cycles (not length 8)

pn10.draw November 30, 1996

937

735

333

length 6

length 10

length 18

length 10

333

333937

937

length 6

735

735

length 18

118


3 nodes

po10.draw November 30, 1996

346 515 689

515

689

346

515

689

689

346

346

512 6221396

512

622

1396

512

512

622

1396

1396

119

Life phoenix de Bruijn diagram, width 107 nodes

December 1, 1996pp10.draw

547649

547649

720

720

1268

1268

1270

1270

722

722

1268

547

649

722

720

1270

1268

547

649

722

720

1270

649

547

549

720

722 1268

1270

649

547

549

720

722

1268

1270

1268649

549722

1268

120


December 4, 1996pq10.draw

3 nodes

629

700

1685

1694

1685 7001694

1626

941

1626

629

1626

629

1626

941

629 1626 941

121

February 28, 1994ps10.draw

122


bet10a.draw December 7, 1996


2

4

24

9

12

10

14

21

61

30

26

35

40

54

299

384

144

74

65

388

260

801

283

83

95

100

129

301

391

633

784

390

174

153

541

793

1347

299384

1021421

118

299384

18261123

24

1021495

695

148616551826

123


December 6, 1996gam10a.draw

gamma component204 nodes

386

111

119

120

481

109

131

472

135

786

139

164

141

261

145

146

147

189

638

155

160

487

794

49

180

105

56

59

62

385

63

80

42

389

68

231

27

75

104

179

81

228

85

221

359

90

97

178

300

143

122

238

247

250

258

259

919

244

279

896

805

286

1316

290

798

172

185

190

202

740

204

209

213

640

789

526

124

Width 10 - z.dat Linkage list of zero component

= 4 0000000000 4 .......... 0 28 69 161 354 ( 0) 0 13 37 92 211

= 4 0000001000 ......o... 0 28 69 161 354 ( 13) 94....................

+ 4 0000103000 ....o.o... 13 33 73 162 355 ( 94) 115....................

- 000080c000 4 .......... .................... 138 ( 167) 28 33 45 99 212

= 0000008000 4 .......... .................... 167 ( 28) 0 13 37 92 211

= 0000009000 ......o... .................... 167 ( 33) 94....................

= 4 0000010000 * .....o.... 0 28 69 161 354 ( 37) 52 215...............

= 0000018000 * .....o.... .................... 167 ( 45) 52 215...............

= 4 0000030100 .....o.o.. 37 45 78 171 356 ( 52) 219....................

- 000081c000 * .....o.... .................... 138 ( 173) 55 217...............

= 0000038100 .....o.o.. .................... 173 ( 55) 219....................

= * 0000080000 4 .......... ............... 88 365 ( 69) 0 13 37 92 211

= * 0000081000 ......o... ............... 88 365 ( 73) 94....................

= * 0000090000 * .....o.... ............... 88 365 ( 78) 52 215...............

= * 00000b0100 .....o.o.. ............... 91 369 ( 84) 219....................

= 00000c0800 4 .......... .................... 361 ( 88) 69 73 78 110 223

= 00000c1800 ......o... .................... 361 ( 89) 112....................

+ * 0000183000 ....o.o... ............... 89 367 ( 112) 115....................

= 00000d0800 * .....o.... .................... 361 ( 91) 84 225...............

= 4 0000100000 * ....o..... 0 28 69 161 354 ( 92) 127 462...............

= 0000108000 * ....o..... .................... 167 ( 99) 127 462...............

- 000080d000 ......o... .................... 138 ( 170) 101....................= 000010b000 ....o.o... .................... 170 ( 101) 115....................

= * 0000180000 * ....o..... ............... 88 365 ( 110) 127 462...............

= 00001c0800 * ....o..... .................... 361 ( 113) 132 466...............

125

= 4 0000301000 ....o.o... 92 99 110 183 370 ( 127) 469....................

- 000090c000 * ....o..... .................... 138 ( 188) 130 465...............

= 0000309000 ....o.o... .................... 188 ( 130) 469....................

= * 0000381000 ....o.o... ............... 113 373 ( 132) 469....................

= * 0000800000 4 .......... ............... 206 746 ( 161) 0 13 37 92 211

= * 0000801000 ......o... ............... 206 746 ( 162) 94....................

= * 0000810000 * .....o.... ............... 206 746 ( 171) 52 215...............

= * 0000830100 .....o.o.. ............... 208 750 ( 176) 219....................

= * 0000900000 * ....o..... ............... 206 746 ( 183) 127 462...............

= * 0000903000 ....o.o... ............... 207 747 ( 184) 115....................

= * 0000b01000 ....o.o... ............... 210 752 ( 201) 469....................

= 0000c08000 4 .......... .................... 742 ( 206) 161 162 171 183 245

= 0000c09000 ......o... .................... 742 ( 207) 184....................

= 0000c18000 * .....o.... .................... 742 ( 208) 176 248...............

= 0000d08000 * ....o..... .................... 742 ( 210) 201 474...............

= 4 0001000000 ...o...... 0 28 69 161 354 ( 211) 273....................

+ 4 0003010000 ...o.o.... 211 212 223 245 394 ( 273) 891....................

= 0001008000 ...o...... .................... 167 ( 212) 273....................

= 4 0001030000 ...o.o.... 37 45 78 171 356 ( 215) 252....................

= 0001038000 ...o.o.... .................... 173 ( 217) 252....................

= * 0001080000 ...o...... ............... 88 365 ( 223) 273....................

= * 00010b0000 ...o.o.... ............... 91 369 ( 225) 252....................

= 00010c0800 ...o...... .................... 361 ( 226) 278....................

+ * 0003090000 ...o.o.... ............... 226 399 ( 278) 891....................

= * 0001800000 ...o...... ............... 206 746 ( 245) 273....................

126

- 0000406080 4 .......... .................... 783 ( 138) 167 170 173 188 246

= 000180c000 ...o...... .................... 138 ( 246) 274....................+ 0003018000 ...o.o.... .................... 246 ( 274) 891....................

= * 0001830000 ...o.o.... ............... 208 750 ( 248) 252....................

- 0080604000 4 .......... .................... 593 ( 742) 206 207 208 210 249

= 0001c08000 ...o...... .................... 742 ( 249) 280....................

+ * 0003810000 ...o.o.... ............... 249 753 ( 280) 891....................

- 4 0001060200 ...o...... 52 55 84 176 357 ( 219) 256....................= 00020c0411 ........oo .................... 219 ( 256) 525....................+ 0015080822 ..oo...... .................... 256 ( 525) 580....................+ 002a000054 * ........o. .................... 525 ( 580) 632 943...............

- * 00450000a2 ...o...... ............... 551 1248 ( 643) 803....................- 008a010144 .....o.o.. .................... 643 ( 803) 284....................= 0004030288 .....o.... .................... 803 ( 284) 361....................+ 0008060400 4 .......... .................... 284 ( 361) 88 89 91 113 226

- 4 0010602000 ..o....... 127 130 132 201 381 ( 469) 535....................- 0020c04110 .......oo. .................... 469 ( 535) 1002....................- 0150808220 .oo....... .................... 535 (1002) 1101....................- 02a0000540 .......o.. .................... 1002 (1101) 1198....................- 0441010a80 ...o.o.... .................... 1101 (1198) 1313....................- 0882030400 .....o.... .................... 1198 (1313) 289....................= 0004060800 4 .......... .................... 1313 ( 289) 365 367 369 373 399

- 000c080000 4 .......... .................... 1242 ( 454) 354 355 356 370 394

= 0008000000 4 .......... .................... 454 ( 354) 0 13 37 92 211

= 0008001000 ......o... .................... 454 ( 355) 94....................

= 0008010000 * .....o.... .................... 454 ( 356) 52 215...............

- 000c090000 * .....o.... .................... 1242 ( 456) 357 395...............

= 0008030100 .....o.o.. .................... 456 ( 357) 219....................

= 00080c0000 4 .......... .................... 289 ( 365) 69 73 78 110 223

= 00080c1000 ......o... .................... 289 ( 367) 112....................

= 00080d0000 * .....o.... .................... 289 ( 369) 84 225...............

= 0008100000 * ....o..... .................... 454 ( 370) 127 462...............

127

- 000c081000 ......o... .................... 1242 ( 455) 371....................= 0008103000 ....o.o... .................... 455 ( 371) 115....................

= 00081c0000 * ....o..... .................... 289 ( 373) 132 466...............

- 000c180000 * ....o..... .................... 1242 ( 458) 381 528...............

= 0008301000 ....o.o... .................... 458 ( 381) 469....................

= 0009000000 ...o...... .................... 454 ( 394) 273....................

= 0009030000 ...o.o.... .................... 456 ( 395) 252....................

= 00090c0000 ...o...... .................... 289 ( 399) 278....................

- 000d080000 ...o...... .................... 1242 ( 461) 447....................= 000b010000 ...o.o.... .................... 461 ( 447) 891....................

= 4 0010300000 ..o.o..... 92 99 110 183 370 ( 462) 530....................

= 0010308000 ..o.o..... .................... 188 ( 465) 530....................

= * 0010380000 ..o.o..... ............... 113 373 ( 466) 530....................

= * 0010b00000 ..o.o..... ............... 210 752 ( 474) 530....................

- 4 0000206010 ........o. 94 101 112 184 371 ( 115) 483....................= 001140c020 ..oo...... .................... 115 ( 483) 551....................+ 0022808051 * ........oo .................... 483 ( 551) 643 698...............

= 0018300000 ..o.o..... .................... 458 ( 528) 530....................

- 4 0002060100 .......o.. 215 217 225 248 395 ( 252) 922....................- 01140c0200 .oo....... .................... 252 ( 922) 1045....................- 0228080510 .......oo. .................... 922 (1045) 1217....................- 0450000a20 ..o....... .................... 1045 (1217) 1349....................- 08a0101440 ....o.o... .................... 1217 (1349) 593....................= 0040302880 ....o..... .................... 1349 ( 593) 742....................+ 0080604000 4 .......... .................... 593 ( 742) 206 207 208 210 249

- * 2a00005400 ......o... ............... 1443 1476 (1569) 1643....................- 441010a800 ..o.o..... .................... 1569 (1643) 1761....................- 8820304000 ....o..... .................... 1643 (1761) 600....................= 0040608000 4 .......... .................... 1761 ( 600) 746 747 750 752 753

= * 00441010a8 ....o.o... ............... 580 816 ( 632) 783....................+ 0088203040 ......o... .................... 632 ( 783) 138....................+ 0000406080 4 .......... .................... 783 ( 138) 167 170 173 188 246

- * 2a00004500 .......o.. ............... 1443 1476 (1568) 1629....................- 4410008a00 ..o....... .................... 1568 (1629) 1731....................

128

- 8820000411 ........oo .................... 1629 (1731) 667....................= 0051000822 ..oo...... .................... 1731 ( 667) 816....................+ 00a2000054 * ........o. .................... 667 ( 816) 632 943...............

= * 00540000a2 ..o....... ............... 551 1248 ( 698) 857....................+ 00a8000144 .......o.. .................... 698 ( 857) 1371....................+ 1140000288 oo........ .................... 857 (1371) 1501....................+ 2280001500 ......oo.. .................... 1371 (1501) 1683....................+ 4500002a00 * .o........ .................... 1501 (1683) 1805 1829...............

= 0080c00000 4 .......... .................... 600 ( 746) 161 162 171 183 245

= 0080c01000 ......o... .................... 600 ( 747) 184....................

= 0080c10000 * .....o.... .................... 600 ( 750) 176 248...............

= 0080d00000 * ....o..... .................... 600 ( 752) 201 474...............

= 0081c00000 ...o...... .................... 600 ( 753) 280....................

= * 01440000a8 .o........ ............... 580 816 ( 943) 1067....................+ 0288001140 ......oo.. .................... 943 (1067) 1443....................+ 1500002280 * oo........ .................... 1067 (1443) 1568 1569...............

- 4 0106020000 .o........ 273 274 278 280 447 ( 891) 1011....................= 020c041100 ......oo.. .................... 891 (1011) 1476....................+ 1508082200 * oo........ .................... 1011 (1476) 1568 1569...............

- * 8a01014400 ...o.o.... ............... 1683 1690 (1829) 1125....................= 0403028800 ...o...... .................... 1829 (1125) 1242....................+ 0806040000 4 .......... .................... 1125 (1242) 454 455 456 458 461

- * 8a00004410 ........o. ............... 1683 1690 (1805) 1157....................= 0411008820 ..oo...... .................... 1805 (1157) 1248....................+ 0822000051 * ........oo .................... 1157 (1248) 643 698...............

- 4 0020601000 ......o... 462 465 466 474 528 ( 530) 1410....................= 1140c02000 oo........ .................... 530 (1410) 1539....................+ 2280805100 ......oo.. .................... 1410 (1539) 1690....................+ 450000a200 * .o........ .................... 1539 (1690) 1805 1829...............

129

11 WIDTH 11

Width 11

pg11 - sample from the zero component

z.dat - zero component connection list

4556 nodes

5640 links

91 components

maximum linkage: 6

consolidated nodes:

zero: 164

alpha 498

beta 498

gamma 405

3-nodes

4-nodes

6-nodes

7-nodes

6-cycles

8-cycles

10-cycles

18-cycles

...

130

2874

235626432874

23562643

4444

1621

1471

1621

259210

4444

264

1471

259264

210

1471

208173221264

Life phoenix de Bruijn diagram, width 11zero component164 nodes

December 20, 1996pg11.draw

857103711923413

4505

29771023

1471

208254103711923413

4444

1471

131

2874

235626432874

23562643

4444

1621

1471

1621

259210

4444

264

1471

259264

210

1471

208173221264

Life phoenix de Bruijn diagram, width 11zero component

164 nodes

December 20, 1996pgg11.draw

857103711923413

4505

29771023

1471

208254103711923413

4444

1471

132


December 1, 1996ph11.draw

gamma component

4552

3721

4178

3828

3473

4379

4456

4392

4386

4400

4391

4388

4393

4178

4178

4552

3721

405 nodes

133


December 25, 1996pj11.draw

30 nodes864

348

1866

1857

1475

1883

1092

1067

1235

1236

1484

1494

1496

1626

1639

1663

1666

2025

2027

1641

3328

2011

4442

4473

4515

3012

3421

3010

3330

348

1235

1236

1484

1639

1857

1092

1067

3421

1475

1626

2011

3010

3012

1641

4442

3098

3099

3330

4473

4515

1494

1663

1866

2025

2027

3328

1883

1496

1666

134


December 25, 1996pk11.draw

24 nodes686

878

1467

1502

1234

1242

1483

1486

1616

1638

1642

1643

1691

3258

1652

4494

4497

3660

4417

4424

3572

3009

3023

3303

1691 1616

6861234

1242

1483

1638

1652

4424

4497

3009

3023

3303

32583660

3672

4417

4494

1502

878

1467

1643

14861642

135


pl11.draw December 25, 1996

726

908

4457

914

1880

782

1395

726

908

914

4457 2746 1469

1618

1492

1661

1880

31973216

2015

1395

782 31873213

1506

1506

1618

1661

2746

3187

3197

2015

782

31871395

1469

1492

3216

3213

1506

2746

18801469

4457

3216

3216

726908

44572746

14691880

31971395

726

2015

2746

1618

136


pm11.draw December 26, 1996

1447

641

3532

2874

2632

2614

1124

1447

641

1124 2317

2316

2614 2632

13141331

2240

2539 35303532

1929

1951

1314

2240

1331

3883

3530

1929

1951

2316

2317

2341

2342

3843

38832341

2342

1124

23162614

253925393530

19292240

137


pn11.draw December 26, 1996

1811

325

1825

537

1449

1321

544

1317

1333

1334

1434

1440

1442

2524

1544

1555

3849

1933

1939

1953

1955

2180

2181

3884

2236

2238

2536

2248

2480

3856

2226

138


pnn11.draw December 26, 1996

1811

325

537

1321

1334

544

1317

1333

1449

1440

2236

1434 2226

2248

3856

1555

2181

1544

2180 2480

2238 2524

2536

1933

1953

1825

3849

3884

1442

1939

1955

3849

22382536

14341825

544

1317

3856

155519552248

139


po11.draw December 26, 1996

1430

1826

631

632

1154

1160

1433

1454

1529

1538

4240

4242

2267

3845

4369

2218

2224

2257

2366

2367

2525

2527

2277

3793

2527

3845

2257 2218

4240

631

1430

4242

2277

140


December 26, 1996poo11.draw

1430

631

632

2218

2277

42404242

43692366

2367

3845

1454

2257

1826

1154

1160

1433

2224

2267

2525 25273793

1529

1538

2267

2218

4369

2366

3793

1538

1538

141


pp11.draw December 26, 1996

1473

598

786

4143

4510

2908

2899

1624

4512

4119

1473 598

786

4143

4510

29082899

1624

4512

4119

4119

1624 786

2899

1473

598786

2908

1473

142


pq11.draw December 26, 1996

1424

630

636

42394251

2211

2281

1424

630

636

4239

42512211

2281

630

636

4239

4251

2211

2281

1424

630

1424

2281

4251

4239

2211

1424

636

2281

4239

636

143

Width 11 - z.dat Zero component connection list

= 5 00000000000 5 ........... 0 28 69 163 370 826 ( 0) 0 13 37 92 213 490

= 5 00000001000 .......o... 0 28 69 163 370 826 ( 13) 94.........................

+ 5 00000103000 .....o.o... 13 33 73 164 372 829 ( 94) 115.........................

- 0000080c000 5 ........... ....................... 139 ( 169) 28 33 45 99 215 493

= 00000008000 5 ........... ....................... 169 ( 28) 0 13 37 92 213 490

= 00000009000 .......o... ....................... 169 ( 33) 94.........................

= 5 00000010000 * ......o.... 0 28 69 163 370 826 ( 37) 52 221....................

= 00000018000 * ......o.... ....................... 169 ( 45) 52 221....................

= 5 00000030100 ......o.o.. 37 45 78 173 375 830 ( 52) 225.........................

+ 5 00001060200 ....o...... 52 55 84 178 376 833 ( 225) 268.........................

- 0000081c000 * ......o.... ....................... 139 ( 175) 55 223....................

= 00000038100 ......o.o.. ....................... 175 ( 55) 225.........................

= * 00000080000 5 ........... .................. 88 386 ( 69) 0 13 37 92 213 490

= * 00000081000 .......o... .................. 88 386 ( 73) 94.........................

= * 00000090000 * ......o.... .................. 88 386 ( 78) 52 221....................

= * 000000b0100 ......o.o.. .................. 91 390 ( 84) 225.........................

- 00008060400 5 ........... ....................... 296 ( 382) 88 89 91 113 233 497

= 000000c0800 5 ........... ....................... 382 ( 88) 69 73 78 110 229 494

= 000000c1800 .......o... ....................... 382 ( 89) 112.........................

+ * 00000183000 .....o.o... .................. 89 388 ( 112) 115.........................

= 000000d0800 * ......o.... ....................... 382 ( 91) 84 232....................

= 5 00000100000 * .....o..... 0 28 69 163 370 826 ( 92) 128 502....................

= 00000108000 * .....o..... ....................... 169 ( 99) 128 502....................

- 00000406080 5 ........... ....................... 894 ( 139) 169 172 175 190 256 516

- 0000080d000 .......o... ....................... 139 ( 172) 101.........................= 0000010b000 .....o.o... ....................... 172 ( 101) 115.........................

+ 5 00000206010 .........o. 94 101 112 186 393 835 ( 115) 529.........................

= * 00000180000 * .....o..... .................. 88 386 ( 110) 128 502....................

= 000001c0800 * .....o..... ....................... 382 ( 113) 133 506....................

= 5 00000301000 .....o.o... 92 99 110 185 391 834 ( 128) 510.........................

- 0000090c000 * .....o..... ....................... 139 ( 190) 131 505....................= 00000309000 .....o.o... ....................... 190 ( 131) 510.........................

= * 00000381000 .....o.o... .................. 113 397 ( 133) 510.........................

= * 00000800000 5 ........... .................. 208 850 ( 163) 0 13 37 92 213 490

= * 00000801000 .......o... .................. 208 850 ( 164) 94.........................

= * 00000810000 * ......o.... .................. 208 850 ( 173) 52 221....................

= * 00000830100 ......o.o.. .................. 210 854 ( 178) 225.........................

= * 00000900000 * .....o..... .................. 208 850 ( 185) 128 502....................

144

= * 00000903000 .....o.o... .................. 209 851 ( 186) 115.........................

= * 00000b01000 .....o.o... .................. 212 856 ( 203) 510.........................

= 00000c08000 5 ........... ....................... 841 ( 208) 163 164 173 185 254 515

= 00000c09000 .......o... ....................... 841 ( 209) 186.........................

= 00000c18000 * ......o.... ....................... 841 ( 210) 178 259....................

= 00000d08000 * .....o..... ....................... 841 ( 212) 203 519....................

= 5 00001000000 * ....o...... 0 28 69 163 370 826 ( 213) 285 1037....................= 00001008000 * ....o...... ....................... 169 ( 215) 285 1037....................

= 5 00001030000 ....o.o.... 37 45 78 173 375 830 ( 221) 264.........................

= 00001038000 ....o.o.... ....................... 175 ( 223) 264.........................

= * 00001080000 * ....o...... .................. 88 386 ( 229) 285 1037....................

= * 000010b0000 ....o.o.... .................. 91 390 ( 232) 264.........................

= 000010c0800 * ....o...... ....................... 382 ( 233) 290 1046....................

= 00001406080 ....o...... ....................... 894 ( 241) 1048.........................+ 0010380c000 ..o.o...... ....................... 241 (1048) 1195.........................+ 00206018000 ......o.... ....................... 1048 (1195) 3413.........................

= * 00001800000 * ....o...... .................. 208 850 ( 254) 285 1037....................

= 0000180c000 * ....o...... ....................... 139 ( 256) 286 1040....................

= * 00001830000 ....o.o.... .................. 210 854 ( 259) 264.........................

= 00001c08000 * ....o...... ....................... 841 ( 261) 292 1047....................

= * 000020c0411 .........oo .................. 225 859 ( 268) 573.........................+ 00015080822 ...oo...... ....................... 268 ( 573) 640.........................+ 0002a000054 * .........o. ....................... 573 ( 640) 716 1115....................

= 5 00003010000 ....o.o.... 213 215 229 254 420 857 ( 285) 1053.........................

= 00003018000 ....o.o.... ....................... 256 ( 286) 1053.........................

= * 00003090000 ....o.o.... .................. 233 425 ( 290) 1053.........................

= * 00003810000 ....o.o.... .................. 261 861 ( 292) 1053.........................

- * 000450000a2 ....o...... .................. 607 1764 ( 727) 915.........................- 0008a010144 ......o.o.. ....................... 727 ( 915) 296.........................= 00004030288 * ......o.... ....................... 915 ( 296) 382 577....................

- * 00441010a80 ....o.o.... .................. 1312 1926 (1444) 1832.........................- 00882030400 ......o.... ....................... 1444 (1832) 301.........................= 00004060800 5 ........... ....................... 1832 ( 301) 386 388 390 397 425 578

= * 00008000000 5 ........... .................. 482 1746 ( 370) 0 13 37 92 213 490

= * 00008001000 .......o... .................. 482 1746 ( 372) 94.........................

= * 00008010000 * ......o.... .................. 482 1746 ( 375) 52 221....................

= * 00008030100 ......o.o.. .................. 484 1750 ( 376) 225.........................

= 000080c0000 5 ........... ....................... 301 ( 386) 69 73 78 110 229 494

= 000080c1000 .......o... ....................... 301 ( 388) 112.........................

= 000080d0000 * ......o.... ....................... 301 ( 390) 84 232....................

= * 00008100000 * .....o..... .................. 482 1746 ( 391) 128 502....................

= * 00008103000 .....o.o... .................. 483 1749 ( 393) 115.........................

= 000081c0000 * .....o..... ....................... 301 ( 397) 133 506....................

145

- 00406081000 .......o... ....................... 4299 (1370) 1757.........................- 0080c103000 .....o.o... ....................... 1370 (1757) 398.........................= 00008206010 .........o. ....................... 1757 ( 398) 529.........................

= * 00008301000 .....o.o... .................. 486 1756 ( 407) 510.........................

= * 00009000000 * ....o...... .................. 482 1746 ( 420) 285 1037....................

= * 00009030000 ....o.o.... .................. 484 1750 ( 421) 264.........................

= 000090c0000 * ....o...... ....................... 301 ( 425) 290 1046....................

= * 0000b010000 ....o.o.... .................. 489 1760 ( 475) 1053.........................

= 0000c080000 5 ........... ....................... 1740 ( 482) 370 372 375 391 420 576

= 0000c081000 .......o... ....................... 1740 ( 483) 393.........................

= 0000c090000 * ......o.... ....................... 1740 ( 484) 376 421....................

= 0000c180000 * .....o..... ....................... 1740 ( 486) 407 580....................

= 0000d080000 * ....o...... ....................... 1740 ( 489) 475 1061....................

= 5 00010000000 ...o....... 0 28 69 163 370 826 ( 490) 651.........................

+ 5 00030100000 ...o.o..... 490 493 494 515 576 919 ( 651) 2090.........................

= 00010008000 ...o....... ....................... 169 ( 493) 651.........................

= * 00010080000 ...o....... .................. 88 386 ( 494) 651.........................

= 000100c0800 ...o....... ....................... 382 ( 497) 655.........................

+ * 00030180000 ...o.o..... .................. 497 578 ( 655) 2090.........................

= 5 00010300000 ...o.o..... 92 99 110 185 391 834 ( 502) 584.........................

= 00010308000 ...o.o..... ....................... 190 ( 505) 584.........................

= * 00010380000 ...o.o..... .................. 113 397 ( 506) 584.........................

= * 00010800000 ...o....... .................. 208 850 ( 515) 651.........................

= 0001080c000 ...o....... ....................... 139 ( 516) 654.........................+ 00030108000 ...o.o..... ....................... 516 ( 654) 2090.........................

+ 5 01060200000 .o......... 651 654 655 664 667 1011 (2090) 2385.........................

= * 00010b00000 ...o.o..... .................. 212 856 ( 519) 584.........................

= 00010c08000 ...o....... ....................... 841 ( 520) 664.........................

+ * 00030900000 ...o.o..... .................. 520 926 ( 664) 2090.........................

= * 00018000000 ...o....... .................. 482 1746 ( 576) 651.........................

= 00018060400 ...o....... ....................... 296 ( 577) 656.........................+ 000301c0800 ...o.o..... ....................... 577 ( 656) 2094.........................+ 01060280000 .o......... ....................... 656 (2094) 2385.........................

= 000180c0000 ...o....... ....................... 301 ( 578) 655.........................

= * 00018300000 ...o.o..... .................. 486 1756 ( 580) 584.........................

= 0001c080000 ...o....... ....................... 1740 ( 581) 667.........................

+ * 00038100000 ...o.o..... .................. 581 1762 ( 667) 2090.........................

- 5 00010602000 ...o....... 128 131 133 203 407 837 ( 510) 591.........................= 00020c04110 ........oo. ....................... 510 ( 591) 1184.........................+ 00150808220 ..oo....... ....................... 591 (1184) 1312.........................+ 002a0000540 * ........o.. ....................... 1184 (1312) 1444 2220....................

- * 0001140c020 ...oo...... .................. 115 398 ( 529) 607.........................= 00022808051 * .........oo ....................... 529 ( 607) 727 784....................

146

- * 00450000a20 ...o....... .................. 1252 2996 (1471) 1881.........................- 008a0101440 .....o.o... ....................... 1471 (1881) 672.........................= 00040302880 .....o..... ....................... 1881 ( 672) 841.........................+ 00080604000 5 ........... ....................... 672 ( 841) 208 209 210 212 261 520

- * 02a00005400 .......o... .................. 2311 2348 (2611) 2852.........................- 0441010a800 ...o.o..... ....................... 2611 (2852) 3138.........................- 08820304000 .....o..... ....................... 2852 (3138) 680.........................= 00040608000 5 ........... ....................... 3138 ( 680) 850 851 854 856 861 926

= * 000441010a8 .....o.o... .................. 640 937 ( 716) 894.........................+ 00088203040 * .......o... ....................... 716 ( 894) 139 241....................

- * 02a00004500 ........o.. .................. 2311 2348 (2610) 2837.........................- 04410008a00 ...o....... ....................... 2610 (2837) 3108.........................- 08820000411 .........oo ....................... 2837 (3108) 753.........................= 00051000822 ...oo...... ....................... 3108 ( 753) 937.........................+ 000a2000054 * .........o. ....................... 753 ( 937) 716 1115....................

= * 000540000a2 ...o....... .................. 607 1764 ( 784) 978.........................+ 000a8000144 ........o.. ....................... 784 ( 978) 2118.........................+ 01140000288 .oo........ ....................... 978 (2118) 2428.........................+ 02280001500 .......oo.. ....................... 2118 (2428) 2897.........................+ 04500002a00 * ..o........ ....................... 2428 (2897) 3189 3217....................

- 000c0800000 5 ........... ....................... 2977 (1023) 826 829 830 834 857 919

= 00080000000 5 ........... ....................... 1023 ( 826) 0 13 37 92 213 490

= 00080001000 .......o... ....................... 1023 ( 829) 94.........................

= 00080010000 * ......o.... ....................... 1023 ( 830) 52 221....................

- 000c0810000 * ......o.... ....................... 2977 (1027) 833 858....................

= 00080030100 ......o.o.. ....................... 1027 ( 833) 225.........................

= 00080100000 * .....o..... ....................... 1023 ( 834) 128 502....................

- 08060400000 5 ........... ....................... 2667 (2977) 1023 1026 1027 1029 1032 1036

- 000c0801000 .......o... ....................... 2977 (1026) 835.........................= 00080103000 .....o.o... ....................... 1026 ( 835) 115.........................

- 000c0900000 * .....o..... ....................... 2977 (1029) 837 920....................

= 00080301000 .....o.o... ....................... 1029 ( 837) 510.........................

= 00080c00000 5 ........... ....................... 680 ( 850) 163 164 173 185 254 515

= 00080c01000 .......o... ....................... 680 ( 851) 186.........................

= 00080c10000 * ......o.... ....................... 680 ( 854) 178 259....................

= 00080d00000 * .....o..... ....................... 680 ( 856) 203 519....................

= 00081000000 * ....o...... ....................... 1023 ( 857) 285 1037....................

= 00081030000 ....o.o.... ....................... 1027 ( 858) 264.........................

- 08060410000 ......o.... ....................... 2667 (2980) 1028.........................- 000c0830100 ......o.o.. ....................... 2980 (1028) 859.........................= 00081060200 ....o...... ....................... 1028 ( 859) 268.........................

= 00081c00000 * ....o...... ....................... 680 ( 861) 292 1047....................

- 000c1800000 * ....o...... ....................... 2977 (1032) 888 1190....................

= 00083010000 ....o.o.... ....................... 1032 ( 888) 1053.........................

= 00090000000 ...o....... ....................... 1023 ( 919) 651.........................

= 00090300000 ...o.o..... ....................... 1029 ( 920) 584.........................

= 00090c00000 ...o....... ....................... 680 ( 926) 664.........................

147

- 000d0800000 ...o....... ....................... 2977 (1036) 1011.........................= 000b0100000 ...o.o..... ....................... 1036 (1011) 2090.........................

= 5 00103000000 ..o.o...... 213 215 229 254 420 857 (1037) 1192.........................

+ 5 00206010000 ......o.... 1037 1040 1046 1047 1061 1190 (1192) 3413.........................

= 00103008000 ..o.o...... ....................... 256 (1040) 1192.........................

= * 00103080000 ..o.o...... .................. 233 425 (1046) 1192.........................

= * 00103800000 ..o.o...... .................. 261 861 (1047) 1192.........................

= * 0010b000000 ..o.o...... .................. 489 1760 (1061) 1192.........................

- 5 00002060100 ........o.. 221 223 232 259 421 858 ( 264) 1090.........................= 001140c0200 ..oo....... ....................... 264 (1090) 1252.........................+ 00228080510 * ........oo. ....................... 1090 (1252) 1471 1621....................

= * 001440000a8 ..o........ .................. 640 937 (1115) 1277.........................+ 00288001140 .......oo.. ....................... 1115 (1277) 2311.........................+ 01500002280 * .oo........ ....................... 1277 (2311) 2610 2611....................

= 00183000000 ..o.o...... ....................... 1032 (1190) 1192.........................

- 5 00106020000 ..o........ 285 286 290 292 475 888 (1053) 1207.........................= 0020c041100 .......oo.. ....................... 1053 (1207) 2348.........................+ 01508082200 * .oo........ ....................... 1207 (2348) 2610 2611....................

- * 08a01014400 ....o.o.... .................. 2897 2904 (3217) 1352.........................= 00403028800 ....o...... ....................... 3217 (1352) 1740.........................+ 00806040000 5 ........... ....................... 1352 (1740) 482 483 484 486 489 581

= 00406080000 5 ........... ....................... 4299 (1367) 1746 1749 1750 1756 1760 1762

- * 08a00004410 .........o. .................. 2897 2904 (3189) 1398.........................= 00411008820 ...oo...... ....................... 3189 (1398) 1764.........................+ 00822000051 * .........oo ....................... 1398 (1764) 727 784....................

- * 2a000045000 .......o... .................. 3522 3606 (3834) 3978.........................- 4410008a000 ..o........ ....................... 3834 (3978) 4238.........................- 88200004110 ........oo. ....................... 3978 (4238) 1552.........................= 00510008220 ..oo....... ....................... 4238 (1552) 1926.........................+ 00a20000540 * ........o.. ....................... 1552 (1926) 1444 2220....................

= * 00540000a20 ..o........ .................. 1252 2996 (1621) 2018.........................+ 00a80001440 .......o... ....................... 1621 (2018) 3317.........................+ 11400002880 oo......... ....................... 2018 (3317) 3673.........................+ 22800015000 ......oo... ....................... 3317 (3673) 4115.........................+ 4500002a000 * .o......... ....................... 3673 (4115) 4444 4505....................

= 0080c000000 5 ........... ....................... 1367 (1746) 370 372 375 391 420 576

= 0080c001000 .......o... ....................... 1367 (1749) 393.........................

= 0080c010000 * ......o.... ....................... 1367 (1750) 376 421....................

= 0080c100000 * .....o..... ....................... 1367 (1756) 407 580....................

= 0080d000000 * ....o...... ....................... 1367 (1760) 475 1061....................

= 0081c000000 ...o....... ....................... 1367 (1762) 667.........................

- 5 00020601000 .......o... 502 505 506 519 580 920 ( 584) 2157.........................= 01140c02000 .oo........ ....................... 584 (2157) 2472.........................+ 02280805100 .......oo.. ....................... 2157 (2472) 2904.........................+ 0450000a200 * ..o........ ....................... 2472 (2904) 3189 3217....................

= * 01440000a80 .o......... .................. 1312 1926 (2220) 2534.........................+ 02880011400 ......oo... ....................... 2220 (2534) 3522.........................+ 15000022800 * oo......... ....................... 2534 (3522) 3834 3836....................

- * 8a000044100 ........o.. .................. 4115 4130 (4444) 2751.........................= 04110088200 ..oo....... ....................... 4444 (2751) 2996.........................+ 08220000510 * ........oo. ....................... 2751 (2996) 1471 1621....................

- * 020c0411000 ......oo... .................. 2090 2094 (2385) 3606.........................

148

= 15080822000 * oo......... ....................... 2385 (3606) 3834 3836....................

- * 1140c020000 oo......... .................. 1192 1195 (3413) 3768.........................= 22808051000 ......oo... ....................... 3413 (3768) 4130.........................+ 450000a2000 * .o......... ....................... 3768 (4130) 4444 4505....................

= * 2a000054000 ......o.... .................. 3522 3606 (3836) 4016.........................+ 441010a8000 ..o.o...... ....................... 3836 (4016) 4299.........................+ 88203040000 * ....o...... ....................... 4016 (4299) 1367 1370....................

= * 8a010144000 ...o.o..... .................. 4115 4130 (4505) 2667.........................+ 04030288000 * ...o....... ....................... 4505 (2667) 2977 2980....................


149

12 WIDTH 12

Width 12

pg12 - sample from zero component

ph12 - 2 isolated cycles

phh12 - 3 more isolated cycles

pi12 - isolated ideal pair

11229 nodes

14607 links

50 components

150



zero component

8633

8483

10959 7006

5311 3636

1812

866

753

593 676

1729

454 593 2658

9448

7557

449 577 665

2886

6704

7866

2351

10260

558

558

412

412

619 2627

1011410873 6898 7578

6649

683

5925

2851

2283

3835

1799

151



isolated component

7125

7125

7125

7125

5667

5667

5667

5667

4317

4317

4317

4317

152


February 20, 1994phh12.draw

isolated component

4316

4316

4316

4316

2994 5853

4824

4824

4824

4824

153



isolated component

12 nodes

1652

1829

2994

3862

10043

4315

6890

5853

10315

7480

10317

9143

10043

5853

10043

5853

10315

4315

10315

4315

10317

7480

9143

1652

100432994 5853

10315 10317

1829

3862 4315

6890

9143

7480

154

Documents

PhxDraw - CINVESTAVdelta.cs.cinvestav.mx/~mcintosh/cellularautomata/Papers... · 2011. 10. 4. · p8x.draw February 14, 1994 width 4 width 5 width 6 width 7 width 8 width 9 width