lorenz_part03_statistics.pdf

Statistics ‘Fractals and Fractal Architecture’

Vienna, 2002 – page 121– Wolfgang E. Lorenz

StatisticsThe different characteristics, qualities and dimensions of images of floor plans and elevations of

buildings have been registered and then analyzed with ‘SPSS for windows’ subsequently.

9.1 The Data-Sheet

Each data-sheet consists of a ‘general part’ with information about the building, including: -) the

name of the object , -) the village or town where it can be found, -) the architect if known, -) the year

of construction – mostly the year of beginning –, -) the size – area in m2 –, -) the reference – in

which source, publication the image can be found –, -) the kind of origin of the plan – e.g. out of a

book or original plans –, -) the description – which means the house type like one-family house,

terrace house, double house, farmhouse, dwelling-building, dwelling and office building, church,

site-plan and town-plan –, -) the quality – whether the walls of a floor plan are painted black, grey

or kept white –, -) if the floor plan includes furniture – the possibilities are: without any furniture,

with sanitary fixtures only, with sanitary fixtures and partially other furniture and with both, sanitary

fixtures and other furniture –, -) if the floor plans include tiles – the possibilities are: terrace-tiles

only, sanitary-tiles only, both, sanitary- and terrace tiles or no tiles –, -) the environment – if the

surrounding nature, e.g. a tree, but also neighboring buildings are taken into consideration in floor

plans and elevations –, -) the kind of presentati on – floor plan, elevation, section, site-plan –, and

additional information about -) the floor-number – storey – and -) the direction of the elevation.

general part / general information about the building

dimension

Benoit

Fractal DimensionCalculator

‘DOS’

floor plan

elevation

The two categories ‘floor plan data’ and ‘elevation data’ on the right side of the data sheet again give

additional information about the image: e.g. about -) the roofline – if the floor plans show broken or

unbroken roof lines –, -) the rectangularity – if the image looks orthogonal , partially grown or naturally

grown –, -) the presence of an annex , -) if there is any symmetry in the floor plans, -) if there is any

symmetrical distribution of the windows in the case of elevations, -) the presence of wooden gables or

sight masonry , -) whether or not it is a gable-elevation, and information about -) the facade – whether

it is smooth, partially structured or structured. Beyond that, the definition factor , the number of pixels for

statistics ‘Fractals and Fractal Architecture’


X- and Y- direction of the bitmap and the scale is given for each image for the computer programs

‘Benoit ’ – using bmp-files –, ‘Fractal Dimension Calculator ’ – using pict-files – and ‘Program to Calculate

Fractal Dimension – ‘DOS’ ’ – using bmp-files with a certain maximum size. Finally the dimensions of

the floor plans, elevations and site-plans have been calculated and supplied with information about the

slope – either the log-log curve of the number of boxes versus the number of base-line-boxes is

diverging or smooth in comparison to the replacing line – and about the procedure, that is the way how

the dimension is calculated – including the smallest box-size in pixels, the box number of the starting

observation and the direction, which means if the smaller or greater box-sizes are used for calculation.

9.1.1 The Aim

The interest, the aim of the data set, is to find out possible influences of certain variables, e.g.

that of house type, size and roughness of the elevation, on the box counting dimension. Tile

lines in a floor plan for example may be interpreted as an additional information which may lead

to a higher dimension – which it actually does as we will see later in this paper. By that it might

be possible to make some classifications with regard to the resulting dimensions, for example

family houses have a wider range of dimensions – that is there are many different possibilities

of design, from smooth to very rough examples – in contrast to terrace houses, which have a

lower range. Another classification may be done with regard to times or styles, e.g. it seems that

Gothic buildings have a higher dimension than modern buildings.

9.1.2 The Dimension

The three graphs on the right show the different

possible slopes of the log-log curve. The continued

curve with the dots offers several points of the

measurement – occupied boxes versus side length. A

straight line, the dotted trend line, which is the average

line, replaces this curve – the slope of this dotted line

determines the fractal dimension. In the data-sheets the

slope stands for the distribution of measured points –

the dots of the graph – of the log-log graph: if all of them

are situated on the replacing line, the ‘slope’ is called

very smooth; if some of them lie a little bit away, it is

called smooth; finally if some points are situated even

farther away from the average-line, it is called

diverging. This last category is excluded from further

research, because the results are too inaccurate. In

general bigger box-sizes – on the left sides of the

graphs – cause lines diverging more often.

9.1.3 The Data

3453 sets of data of 1178 different buildings have been

prepared in this evaluation. These sets of data have been

analyzed with the aid of the computer program ‘SPSS for

windows’, using different comparisons of variables and

dimension, e.g. the roughness of elevation is compared

with the dimension-category, or the dimension is put

opposite the quality of floor plans.

smooth

very smooth

diverging



The minimum-, the maximum- and the mean value alone do not give us any exact conclusion.

So it is much better to consider the box-plot graphs on the following pages, which show the median,

quartiles, and extreme values. The box represents the interquartile range, which comprises 50% of

the values. The upper and lower lines indicate the highest and lowest values, excluding outliers; the

thicker line across the box indicates the median. The median represents the value above and below

which half the cases fall – that is the 50 percentile – and the 95% confidence-interval of the mean

value is the region where the real mean value is situated including the outliers – the ‘real mean

value’ is positioned within this interval with a possibility of 95%.

In the following the data are separated in two different sets, one that relates to the ‘ Benoit ’ data

set and the other to the ‘Fractal Dimension Calculator ’. Both computer-programs use the box-

counting method, with ‘Benoit ’ running under ‘windows’ and ‘Fractal Dimension Calculator ’ on

‘apple-computers’. In the following section first the results of the floor plans for ‘Benoit ’ (I) and the

‘Fractal Dimension Calculator ’ (II) are given, and then those of the elevations, again for both

computer-programs (III/IV).

9.2 The Evaluation

9.2.1.a I) House Types – Dimension – Floor Plan – ‘Benoit’

The first example compares the dimensions with regard to the method – this stands for the

computer-program –, the house type and the slope. Looking at the table below right we can

separate the data of the mean values of house types into three different categories:

1st category consists of the house types:

double houses (*);

terrace houses;

one-family houses;

farmhouses;

In this category the calculated mean values lie between 1.48

and 1.50. All examples of house types of this category belong to

the group of smaller buildings with fewer rooms counted.

2nd category consists of the house types:

dwelling buildings (*);

public buildings (*);

office and public buildings (*);

In this category the calculated mean values lie between 1.53

and 1.56. The reason for the higher dimension of the floor plans

of these house types may lie in the higher scale of the plans,

which means more information on a smaller space, bigger

drawn lines with regard to the empty rooms in between and

mostly black drawn walls and in the bigger size of the house

types themselves.

3rd category consists of

town-plans (*) with a calculated mean value of 1.64.

The set of house types which are marked with a star (*) only include a few examples –

compare with the table right above, where ‘N’ is the number of examples. Because of that it is

hard to make an evaluation, but the results nevertheless offer a direction, which means that a

tendency can be seen.



The Values

Symmetrical distribution of the box-plot

indicates that the real mean value and the

calculated mean value of the 95% confidence

interval are quite similar. In this sense the

examples of one-family houses, towns and

terrace houses are symmetrically distributed

in contrast to double houses and public

buildings whose medians fall low with regard

to their interquartile range – see the box-plot

on the right.

For example the median of double houses,

which is 1.475, is smaller than the calculated

mean value, being 1.484. This means that

there are more examples – floor plans – below

the calculated mean value than above it. This

causes a smaller real mean value than 1.484.

But for this house type there are too few values

– ‘N’=28 –, for making an exact conclusion.

In the case of farmhouses the median

results in 1.49 and the calculated mean value

in 1.478, which indicates that there are more

examples above the calculated mean value.

Following from that, the real mean value is

bigger than 1.478. The reason for this

difference is that the distribution of the

dimensions consists of more than one peak in

the curve – there are two regions with an

accumulation of values; see the image right

below. The first ranges from 1.39 to 1.44 and

the second from 1.50 to 1.59.

For the cases of terrace houses and one-

family houses the calculated mean value –

1.50 and 1.48 respectively – and the median –

1.50 and 1.48 respectively – are identical,

which is an indication for the ‘correctness’ of

the values. Besides the number of examples

are 117 respectively 397, which is enough for

making an evaluation.

The box-plot graph also tells us that in the cases of farmhouses – from 1.42 to 1.56 – and

terrace houses – from 1.43 to 1.56 – the 50%-box-range reaches from smoother to rougher

examples – so there is a bigger spread of different types, means roughness, of floor plans.

9.2.1.b II) House Types – Dimension – Floor Plan – ‘Fractal Dimension Calculator’

In sum there are more values present than for the ‘Benoit ’ data set. But nevertheless the same

tendency and similar separation into three categories can be done, with one exception: the terrace

house type this time belongs to the second category.



1st category consists of the house types:

double houses (*); one-family houses; farmhouses;

the calculated mean values lie between 1.437 and 1.456.

2nd category consists of the house types:

terrace houses; dwelling buildings (*); public buildings (*); office and public buildings (*);

the calculated mean values lie between 1.49 and 1.52.

3rd category consists of

town-plans (*) with a calculated mean value of 1.64.

In general the dimensions of the ‘Fractal Dimension Calculator ’ program are smaller than

those of the ‘Benoit ’ program, except in the cases of terrace houses and towns where they remain

the same.

9.2.1.c III/IV) House Types – Dimension – Elevation – ‘Benoit’ & ‘Fractal Dimension Calculator’

For most house types in this category there are too few values to draw some conclusions,

except for the farmhouses. The calculated mean value of the ‘Benoit ’ program is 1.533 and that

of ‘Fractal Dimension Calculator ’ 1.527, which is quite similar. The calculated mean values for

the floor plans are much smaller, namely 1.478 for ‘ Benoit ’ and 1.456 for ‘Fractal Dimension

Calculator ’. That says something about the higher degree of information of elevations. The

conclusion from that may be that for farmhouses the elevations are ‘rougher’, because of

wooden elements, asymmetric parts and sight masonry, than the floor plans. In any case the

ratio of empty areas with regard to black lines – or filled areas of walls – in the floor plans is

higher than for elevations.

9.2.2.a I/II) Furniture – Dimension – Floor Plans – ‘Benoit’ & ‘Fractal Dimension Calculator’

The more furniture is present in the plans, the higher the dimension is. This means that the more

lines can be found in a plan the more information is given to us. But there is also another observation,

namely that if no furniture is present, the dimension is higher than with sanitary fixtures. The reason

may be that the plans of the first category are in general on a smaller scale with black painted walls,

which would mean a higher percentage of thicker lines of walls in respect to the ‘white’ rooms.

The calculated mean values are:

‘without furniture’: ‘Benoit ’: 1.495; ‘Fractal Dimension Calculator ’: 1.467

‘only sanitary fixtures’: ‘Benoit ’: 1.466; ‘Fractal Dimension Calculator ’: 1.428

‘partially’: ‘Benoit ’: 1.499; ‘Fractal Dimension Calculator ’: 1.439

‘with furniture’: ‘Benoit ’: 1.543; ‘Fractal Dimension Calculator ’: 1.562

9.2.3.a I/II) Tiles – Dimension – Floor Plans

– ‘Benoit’ & ‘Fractal Dimension Calculator’

Though for the categories ‘with tiles’ and ‘with

terrace tiles’ there are only a few examples –

‘N’=30 for ‘Benoit ’ –, it nevertheless underlines

the tendency of increasing dimension by

increasing tiles. But the same phenomenon as in

the previous category can be found, namely that

if no tiles are drawn, the dimension is higher than

with sanitary-tiles. This may also result from a



smaller influence of sanitary-tiles, because if both, terrace- and sanitary-tiles are present, the

dimension unequivocally increases for ‘Benoit ’ from 1.52 to 1.585 – for the ‘Fractal Dimension

Calculator ’ it even decreases.


‘without tiles’: ‘Benoit ’: 1.483; ‘Fractal Dimension Calculator ’: 1.456

‘with terrace-tiles’: ‘Benoit ’: 1.520; ‘Fractal Dimension Calculator ’: 1.573

‘with both tiles’: ‘Benoit ’: 1.585; ‘Fractal Dimension Calculator ’: 1.540

Comparing the values of ‘Benoit ’ with the results for the computer-program ‘Fractal Dimension

Calculator ’ shows that the ranges of the box-counting dimension for ‘tiles’ are not far away from each

other: for the category ‘without tiles’ the calculated mean value of the dimensions for the images is

1.456 for ‘Fractal Dimension Calculator ’ and 1.483 for ‘Benoit ’, which is only a little bit higher.

9.2.4.a I) Quality – Dimension – Floor Plans – ‘Benoit’

The color of the walls has an obvious

influence on the resulting dimension. For all

categories – black painted walls, grey and white

walls – there are enough values to draw clear

conclusions. The category ‘white walls’ has the

absolutely smallest dimension with a calculated

mean value of 1.426 – once more regarding

dimension as an indication of information, ‘white

walls’ mean two lines without any information for

the user in between. The category ‘grey walls’

interprets this middle part as something with

additional information, which cannot be touched

or seen with eyes but is nevertheless present –

here the dimension increases to 1.472. Finally ‘black walls’ have a calculated mean value of

1.523 – interpreting each part of the wall as additional ‘information’. In all of these three

categories the median and the calculated mean value are close together, which indicates the

exactness of the values.

9.2.4.b II) Quality – Dimension – Floor Plans – ‘Fractal Dimension Calculator’

For the category of ‘white walls’ we only have few values, which may be the reason why in the

case of ‘Fractal Dimension Calculator ’ this category has the highest calculated mean value with

1.500. The other two, the ‘grey walls’ – 1.426 – and ‘black walls’ – 1.482 – show the same tendency

as before. Again the dimensions for ‘Fractal Dimension Calculator ’ are, in general, lower than those

for ‘Benoit ’.

9.2.5.a II) Rectangularity – Dimension – Floor Plans – ‘Fractal Dimension Calculator’

Under the supplement of floor plans it turns out that the fact whether the walls are situated

orthogonally or look naturally grown has not that much influence on the resulting dimension: the

box-counting dimension ranges from 1.487 for ‘rectangular’ plans, over 1.517 for ‘partially

orthogonal’ plans to 1.472 for ‘naturally grown’ examples. ‘Naturally grown’ in this connection

just means that the floor plan is not rectangular but curved or it consists of angles lower or

higher than 90 degrees. None of the results has a symmetrical distribution of the box-plot graph,

especially that of ‘naturally grown’.




‘orthogonal’: ‘Benoit ’: 1.487; ‘Fractal Dimension Calculator ’: 1.458

‘partially orthogonal’: ‘Benoit ’: 1.517; ‘Fractal Dimension Calculator ’: 1.499

‘naturally grown’: ‘Benoit ’: 1.472; ‘Fractal Dimension Calculator ’: 1.481

One conclusion is that rectangularity leads to smaller dimensions than for ‘partial growth’,

which is true for both, ‘Benoit ’ and ‘Fractal Dimension Calculator ’. Then the dimension for

‘natural growth’ is lower than for ‘partial growth’, which can arise from the fewer data available

– ‘Benoit ’: ‘N’=59. In addition to that in case of the ‘Benoit ’ program the presence of more values

in the lower field – the median is situated in the lower part of the box – reduces the real mean

value once more in respect to the calculated one. This is also true for the results of the ‘ Fractal

Dimension Calculator ’ data set, where more data is available – ‘N’=68. But in the latter case the

calculated mean value is higher than the one for the category ‘orthogonal’.

9.2.6.a I) Roofline – Dimension – Floor Plans – ‘Benoit’

Between the categories ‘without’ and ‘partially

lined’ there is no significant difference – 0.006 –,

while the category ‘roofline’ offers a little smaller

dimension, which may once more result from a

smaller number of data – ‘N’=53. Besides the first

two categories offer so-called bell-curves, while

the third is jagged which indicates a bad

distribution.


‘without roofline’: ‘Benoit ’: 1.496

‘part. roofline’: ‘Benoit ’: 1.490

‘with roofline’: ‘Benoit ’: 1.435

9.2.6.b II) Roofline – Dimension – Floor Plans – ‘Fractal Dimension Calculator’

This time the curves offer a distribution of a bell-curve for all three categories, which seems to

be a more realistic result, because it is well balanced. In this case the dimension increases from the

category ‘without’ – 1.460 –, over ‘partially lined’ – 1.491 – to ‘with broken roofline’ – 1.491. The very

small differences between these three values show that the influence of the broken roofline is very

small.

9.2.7.a III/IV) Smoothness – Dim. – Elevation – ‘Benoit’ & ‘Fractal Dimension Calculator’

The results of the elevation-roughness indicates that the smooth elevations have a much lower

dimension – the calculated mean value is 1.369 for ‘Benoit ’ – than the partial rough ones – 1.583. This

proves that the dimension is an indicator of roughness and by that of information. The median of the

category ‘very rough facades’ – with only 39 pieces of data – is situated in the upper part of the box,

so the real mean value is lower than the calculated one, which is 1.667.


‘smooth elevation’: ‘Benoit ’: 1.369; ‘Fractal Dimension Calculator ’: 1.462

‘partially structured’: ‘Benoit ’: 1.583; ‘Fractal Dimension Calculator ’: 1.549

‘structured elevation’: ‘Benoit ’: 1.667; ‘Fractal Dimension Calculator ’: 1.543

9.2.8.a Variables with no Significant Influence on the Dimension

After analyzing the data with ‘SPSS for windows’ it seems that there are some variables,

which have no or only little influence on the dimension, that is they cannot be linked to the fractal

dimension. Beside that the influence may be undiscovered because of too few or too different

examples, e.g. in their quality. ‘Storey’ and ‘scale’ in the case of floor plans, ‘number of floor

plans’ in the case of elevations seems to belong to the first category with no influence, which

does not offer any tendency.

With only few examples the categories ‘environment’, ‘size’ – the tendency, however, shows that

dimension seems to increase with size – and ‘kind’ – the whole object having a higher dimension

than the part – belong to the second category. It also seems that buildings of the year 1900 have a

higher dimension than those of the 1940ies, but again there are not enough examples.

9.3 The Farmhouses

The following examples are taken from the book ‘Alte Bauernhäuser in den Dolomiten’ by

Edoardo Gellner. The original images of the elevations – scanned with a definition factor of

‘300 ppi’ – were analyzed with the computer-program ‘Benoit ’. Those resulting points of the

log-log graph that are situated beside the slope being excluded from measurement – that

reduces the standard deviation, SD, and by that increases the exactness of the replacing line.

On the one hand the results below indicate that the different elevations of one and the

same building may offer different roughness – main-elevation and side-elevation – and that

on the other hand, similar characteristics of elevations lead to similar dimensions which is

underlined by placing a certain letter beside the images: A=dimension above 1.66; B=1.61-

1.65; C=1.56-1.60; D=1.51-1.55; E=1.46-1.50; F=1.41-1.45; G=1.31-1.40; I=1.20-1.30.

example file-name [page] size [pixel] dimension SD:

Zoldaner-Cadoriner type 231a 1138X881 1.681 0.001231h 1547X869 1.581 0.002231i 1165X753 1.568 0.002231j 1401X896 1.466 0.002

house De Sandre in Laggio – rural commune Vigo di Cadore 237a 1150X1115 1.414 0.002237h 1137X1074 1.241 0.003237i 958X1019 1.284 0.003

house Domen in Pelos – rural commune Vigo di Cadore 241e 1381X1065 1.375 0.003241h 1633X1069 1.486 0.003241i 1391X915 1.541 0.003

house Pe d’Ornella in Ornella – r. c. Pieve di Livinallongo 243e 2152X1331 1.633 0.002243g 2101X1322 1.635 0.005

house Mas de Sabe in Mas di Sabe – r. c. Zoldo Alto 245a 1337X723 1.740 0.001245g 1483X641 1.456 0.003245h 1667X734 1.576 0.004

Tabià Fattor in Mareson – rural commune Zoldo Alto 247a 1225X987 1.663 0.004247f 1753X1021 1.617 0.003247i 1535X983 1.692 0.001

Tabià Brustolon in Foppa – rural commune Forno di Zoldo 249e 1576X1116 1.573 0.003249g 2279X1094 1.572 0.003249h 2306X1116 1.516 0.002



Z o l d a n e r - C a d o r i n e r

t y p e

C 1.581 C 1.568 E 1.466A 1.681



h o u s e D o m e n i n P e l o s

G

1 . 3

7 5

E

1 . 4

8 6

D

1 . 5

4 1

h o u s e D e S a n d r e i n L a g g i o

B

1 . 6

3 3

B 1 . 6

3 5

h o u s e M a s d e S a b e

i n M a s d i S a b e

A

1 . 7

4 0

F

1 . 4

5 6

C 1 . 5

7 6

T a b i à F a t t o r i n M a r e s o n

A

1 . 6

6 3

B 1 . 6

1 7

A

1 . 6

9 2

T a b i à B r u s t o l o n i n F o p p a

C 1 . 5

7 3

C 1 . 5

7 2

h o u s e D e S a n d r e i n L a g g i o

F

1 . 4

1 4

I 1 . 2

4 1

I 1 . 2

8 4



The tables on the following pages compare the dimensions of elevations – the images are taken

from ‘Alte Bauernhäuser in den Dolomiten’ and scanned with ‘300 ppi’ – measured with the

computer-program ‘Benoit ’, using an increment of grid rotation of 15 degrees, with those measured

with an increment of grid rotation of 0 degrees and the computer-programs ‘Fractal Dimension’,

‘Fractal Dimension Calculator ’ and ‘Program to Calculate Fractal Dimension’ respectively. For all

measurements with ‘Benoit ’ the smallest three and largest three box-sizes were excluded from

calculation to increase the exactness of the replacing line. The results of the tables indicate that the

five dimensions, calculated for every image, are more or less the same – those values, which

diverge by a value more than 5% with regard to the ‘original result’ of the first row are pointed out

by numbers in italics and by underlining them, those that diverge more than 10% are put into

brackets –, the ‘Fractal Dimension Calculator ’ being the program which diverge most.

example size ‘Benoit’ ‘Benoit’ ‘Fract. Dim.’ ‘Fract. Dim. Program to(all page 122) [pixel] 15° rotation; 0° rotation; Calculator’ Calculate ...’

dim./SD dim./SD dimension dimension dimension

GS5_1 – rural commune Gosaldo 549X405 1.282/0.002 1.270/0.006 1.285 1.310 1.25±0.06

LI4_1 – rural commune Livinallongo 389X441 1.311/0.004 1.306/0.006 1.326 1.30±0.06

CA8 – rural commune Cortina 549X501 1.342/0.005 1.337/0.005 1.323 1.468 1.29±0.06

GS3 – rural commune Gosaldo 477X293 1.344/0.001 1.347/0.002 1.340 1.434 1.29±0.05

RA2 – rural commune Rivamonte 341X377 1.351/0.001 1.348/0.001 1.374 1.454 1.39±0.08

GS4 – rural commune Gosaldo 489X285 1.353/0.001 1,354/0.001 1.381 1.484 1.33±0.13GS2 – rural commune Gosaldo 333X340 1.370/0.000 1.363/0.000 1.384 1.37±0.12

GS1 – rural commune Gosaldo 557X465 1.382/0.001 1.383/0.001 1.411 1.499 1.38±0.03

ZA4 – rural commune Zoldo Alto 653X377 1.379/0.001 1.375/0.002 1.394 1.39±0.06

ZA2 – rural commune Zoldo Alto 545X389 1.385/0.001 1.378/0.002 1.412 1.482 1.38±0.13


CE3 – rural commune Cencenighe 389X433 1.392/0.002 1.388/0.004 1.387 1.302 1.37±0.09

The elevations above show similar buildings in the way that the surfaces are mostly smooth

with the only ‘information’ given by windows and few balconies. This causes similar dimensions,

which remain within a range from 1.28 to 1.40 – ‘original results’ of the first row.



ZA1 – rural commune Zoldo Alto 601X389 1.424/0.002 1.425/0.002 1.449 1.41±0.06


AL1 – rural commune Alleghe 649X409 1.442/0.003 1.440/0.003 1.456 (1.595) 1.44±0.03

CE2_2 – rural commune Cencenighe 369X437 1.449/0.001 1.449/0.001 1.470 1.49±0.05

ZA3 – rural commune Zoldo Alto 605X380 1.452/0.005 1.440/0.003 1.510 (1.618) 1.55±0.11FA1 – rural commune Falcade 505X701 1.453/0.004 1.452/0.005 1.485 1.597 1.47±0.19

FA2 – rural commune Falcade 525X472 1.455/0.005 1.454/0.006 1.454 1.544 1.45±0.17


LI7 – rural commune Livinallongo 557X457 1.477/0.006 1.471/0.007 1.479 1.506 1.48±0.23

FA6_1 – rural commune Falcade 445X381 1.478/0.002 1.481/0.003 1.493 1.387 1.39±0.09

BR2 – rural commune Bramezza 801X477 1.499/0.001 1.499/0.001 1.506 1.486 1.47±0.02

GS5_1 LI4_1 CA8 GS3 RA2 GS4 GS2

GS1 ZA4 ZA2 RA3 CE3

The examples above and below – the images of the latter are given on the upper part of the next

page – are much more structured than the previous ones – balconies, wooden paneling and

wooden gables – and they are mostly not symmetric. The ‘original results’ of the first row ranges

from 1.505 to 1.553 and from 1.556 to 1.579 respectively.






SV4 – rural commune S. Vito 525X472 1.566/0.001 1.548/0.00 1.567 1.537 1.58±0.07

LI1 – rural commune Livinallongo 649X409 1.562/0.001 1.551/0.00 1.577 1.541 1.60±0.05SV3 – rural commune S. Vito 369X437 1.572/0.005 1.576/0.00 1.594 1.584 1.65±0.02

SV1 – rural commune Alleghe 793X417 1.578/0.000 1.578/0.00 1.591 1.549 1.61±0.03

GS5_2– rural commune Gosaldo 269X245 1.579/0.000 1.574/0.00 1.583 (1.327) 1.45±0.08



The examples below all offer a smooth facade with a larger portion of balconies in respect to

the first group, situated in the upper storeys. The only exception is the 9 th elevation, which is very

smooth on the left and regularly structured on the other half. In addition to that most of these

elevations are more or less symmetric.




ZA5 – rural commune Zoldo Alto 241X345 1.511/0.004 1.507/0.003 1.554 1.515 1.59±0.19

LI2 – rural commune Livinallongo 569X401 1.513/0.006 1.511/0.006 1.539 1.581 1.56±0.32 AL2 – rural commune Alleghe 525X520 1.517/0.003 1.515/0.004 1.533 1.507 1.48±0.14

CE1 – rural commune Cencenighe 601X389 1.524/0.005 1.520/0.004 1.551 1.593 1.54±0.23

GO6 – rural commune Goima 709X673 1.527/0.006 1.528/0.007 1.535 1.590 1.60±0.11

BR1 – rural commune Bramezza 637X405 1.529/0.002 1.511/0.002 1.533 1.545 1.53±0.02



ZA1 RA1 AL1 CE2_2 ZA3 FA1 FA2

CA9 LI7 FA6_1 BR2

FA5 ZA5 LI2 AL2 CE1

GO6 BR1

LI5

CA5





FA4 – rural commune Zoldo Alto 729X445 1.610/0.001 1.610/0.001 1.605 1.539 1.60±0.07 AL3 – rural commune Cencenighe 789X441 1.611/0.005 1.614/0.005 1.615 1.533 1.56±0.02




CA4 – rural commune Cortina 585X337 1.612/0.004 1.614/0.003 1.595 1.56±0.36

BC2 – rural commune Falcade 605X464 1.640/0.003 1.639/0.004 1.644 1.581 1.66±0.06

SV_2 – rural commune Falcade 693X497 1.648/0.003 1.649/0.003 1.647 1.616 1.68±0.04

The elevations on this page are mostly structured – large parts being made of wooden elements

– and the symmetric, smooth parts are minimized.



CE2_1 – rural commune Cortina 373X349 1.657/0.004 1.653/0.004 1.663 1.590 1.65±0.18CA1 – rural commune Cortina 645X421 1.666/0.007 1.654/0.008 1.642 1.595 1.67±0.09

BC1 – rural commune Borca 629X493 1.670/0.002 1.668/0.002 1.664 1.627 1.65±0.06

CA7 – rural commune Livinallongo 537X400 1.672/0.008 1.672/0.008 1.651 1.531 1.66±0.35

FA6_2 – rural commune Falcade 433X285 1.740/0.007 1.736/0.008 1.749 (1.516) 1.70±0.15

LI4_2 – rural commune Zoldo Alto 389X441 1.751/0.005 1.740/0.004 1.733 1.584 1.71±0.33

CA3 CA6 CA2 SV4 LI1

SV3 SV1 GS5_2

FA4 AL3 FA3 LI6

LI3 CA4 BC2 SV_2

CE2_1 CA1 BC1 CA7 FA6_2 LI4_2















Documents

lorenz_part03_statistics.pdf