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Symmetries in the Mind: Production, Perception, and Preference for Seven One-DimensionalPatternsAuthor(s): Dorothy Washburn and Diane HumphreySource: Visual Arts Research, Vol. 27, No. 2(54) (2001), pp. 57-68Published by: University of Illinois PressStable URL: http://www.jstor.org/stable/20716037 .
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Symmetries intheMind: Production,Perception, andPreference forSeven One-Dimensional Patterns
DorothyWashburn
Maryland Institute,ollege ofArt
Diane HumphreyKing'sCollege
Abstract
Cultural factorsaffecting perception of the
differentymmetryombinations inthesevenone-dimensional band patterns were studied by
givingproduction,preferenceand perceptiontasks to art students and students untrained in
art. They first onstructed patterns on paper from
paper trianglesbefore and after training in
symmetry motions, preferences and amount-of
symmetry ratings of the patterns were taken.
Production, preference, and perception results
differed.Artistsmost frequentlyproducedvertically reflective symmetries while non-art
students produced bifold rotations mostfrequently.While all participants preferredpatterns that have symmetries known to have
greater salience (mirror eflection), nly artstudents also preferredless salient typesof
symmetriesbifold otation,lide reflectionnd
translation).
Symmetry inform is remarkable for its
ubiquity inboth nature and culturallyproduced objects (Enquist & Arak, 1994;
Hargittai&
Hargittai, 1994; Stevens, 1974;Washburn & Crowe, 1988). Mate selection
among several species (e.g.Moeller, 1992;Swaddle & Cuthill, 1993) appears to bedriven bybilateral symmetryofbody form,
possibly a characteristic of healthierorganisms and thusmore desirable as a con
tributorfmore viable genes for the next
generation (Thornhill& Gangestad,1993).Human beings also show specific discrimination and preference in terms of visual
lookingtimefor erticalmirrorreflection searly as fourmonths of age when symmetries are presented in dot patterns(Humphrey & Humphrey, 1989) and as
images of faces (Muir, Humphrey &
Humphrey, 1994). Symmetry in faces islikewisepreferredbyadults in estern andnon-Western cultures
(Rhodeset. al.,
2001).However, the special salience of verti
cal reflectionhas ledsome researchers to
focus on thissymmetryperhaps because itiseasier to detect (Baylis & Driver, 1994,2001; Bertamini, Freidenberg & Kubovy,1997; Freidenberg & Bertamini, 2000).
Other researchers compared finite nits in
vertical reflection timulito linearrepetitions,
implyinghatrepetitions ere notgenerated
by symmetries (Bruce & Morgan, 1975;Corballis & Roldan, 1974, cf.Fig. 1).
But since repeated patterns are generated by a number of symmetries and all of
these are knownand have been completelyderived and described (Grunbaum &
Shepard, 1987) and are used by culturesall over theworld toproduce repeated patterns (cf.Washburn & Crowe, 1988) testsofsymmetry erception should encompass
all of these symmetrymotions and motioncombinations.
One point of confusion inpast studieshas been a researcher's failure to be ex
plicit bout whether he or she was testingthe difference between perception of thefoursymmetrymotions?mirror reflection,rotation,translation,and glide reflection?or the perception of the differentwaysthese fourmotions can be combined to
produce one- and two-dimensional planepatterns. There are seven ways that re
peated symmetricpatterns can result fromthe repetitionof the fourbasic symmetrymotions along a single linear axis. Mathematicians call these seven unique com
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binations of the fourmotions one-dimen
sional infinitepatterns. Likewise, the 17
"wallpaper" patterns that re formedby the
repetitionof these fourmotions along in
tersecting linear xes are called two-dimensional infiniteatterns. Most studies have
attended to theperception of the fourmo
tions,although as noted above, some re
searchers confused the issue by compar
ingperception of single symmetrical units
with linearpatterns created by combiningsome of these motions.
We wish toadd to the study of symme
try erception byoffering tudies thatcon
sider the cultural factors thatmay
affect
symmetryperception and preference. The
studies to date of this issue have reported
conflicting results. Washburn (1999, in
press) and Washburn and Crowe (2002)offercase studies of preferences forcer
tainsymmetries indifferent ultural situa
tions. Incontrast, incross-cultural tests,
Deregowski (1972) found Zambi?n
children's reproductions of patterns with
mirrorsymmetries did not differfrom imi
lar tudies in estern cultures. Rentschler,Juttner, nzickerand Landis (1999) found
mirror symmetry preference to be unaf
fected by category learningand thus con
cluded that symmetry preference ingeneral is innate. Inthispaper we seek tobalance our understanding of the basic hu
man preference forvertical reflection- n
apparently universal perceptual character
istic- ith explorations thatbegin to detail
thecultural factors thatcan
affect production fsymmetricpatterns and preferencesfordifferent ymmetries.We offer everal
kinds of tests that expose the difference
between symmetrysalience as a function
of perception and differential symmetry
preference as a functionof differentcul
tural factors.We have developed tests that show
viewers with two kinds of cultural experiences with pattern (artists nd non-artists)thecomplete array ofsymmetries thatgenerate linear,banded designs. There are
seven combinations of the fourmotions that
generate these one-dimensional patterns:translation (p111), verticalmirrorreflection
(pm11), horizontalmirrorreflection(p1m1),horizontal and verticalmirrorreflectionnd
bifold rotation (pmm2), bifold rotation
(p112), verticalmirror reflection nd bifold
rotation pma2), and glide reflection p1a1)(see Figure 1).We use the standard no
menclature of Washburn and Crowe
(1988). We test for ifferences in rtist and
non-artist production of patterns usingthese seven symmetries as well as for if
ferences in theirpreferences for theseseven symmetries.Our thesis is that if he
salience of differentkinds of symmetriesisentirelya perceptual issue, then the re
sponsesof the artists and non-artists
should not be significantlydifferent. on
versely, ifultural factors ffectpreference,then the responses of the artists and non
artists will differ. If ymmetry preferencevaries, thenwe need to explore the fac
tors that ffect thispreference.Inthisstudywe explore the effectartis
tictraining as on symmetry erception and
symmetrypreference by asking artists and
a control group of non-artists to respond
to visual arrays of patterns as well asto create patterns. We considered that
training in formreceived by artistswould
constitute one of the factors that charac
terizes and thus differentiates the visual
looking and creating activities of artistsfrom ther individuals. Infact, ithas been
previously observed by Nodine, Locher,and Krupinski (1993) that rtists focusmore
on design characteristics in representational
images,while untrained observers
focusmore on individual bjects in the im
ages. But, since they nly tested responsesto representational images, we wanted to
know whether this focus on composition is
also active when artists create and view
non-representational patterns by exploringwhether symmetry isone of these compositionaldesign features.But, in rder to test
whether symmetryprocessing for rtists is
perceptually and/or culturally based, we
need to test for the differentkinds of per
ceptual and cognitive skills used by artists
and non-artists. Thus, it is necessary to
present both artists and non-artists with
requests toproduce a pattern from hapes
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(something that artists do) and also to re
quest them to inspect visually a set of
shapes already arranged in a pattern
(something thatboth artists and non-art
istsdo routinely). In thisway we could isolate responses thatwere peculiar to those
individuals having special training that
might relate todifferentkinds of symmetryuses and preferences.
Method
Participants
Fifty-one tudents at theMaryland InstituteCollege of Art (MICA) inBaltimore, Maryland: 25 females (mean age = 23.6 years,SD = 5.6) and 26 males (mean age
= 22.4
years, SD =3) participated in hestudy.The
Maryland Institute sa four-year tudio art
college where students receive instructionin arious art-makingmedia and receive a
BFA degree. Thirty-eightnon-art students
fromKing's College who had no post-sec
ondary art training: 2 females (mean age= 21.5 years, SD = 5.6) and 6males (meanage = 21.1 years, SD= 1.1) participated inthe study. King's College isa liberal arts
affiliate of the University ofWestern
Ontario, where graduates receive a B.A.
Training inspecific one-dimensional symmetries isnotpartof eitherMICA orKing'sstudents' regular curricula.
Procedure
Participantswere either tested individuallyor at individual esks in classroom where
theywere requested not to look at eachother'swork.The first askwas toconstructband patternswith right riangles cut fromcontact paper. Each participantmade onlyone design. They were thenasked to rateand rank theirpreferences for completearray of the seven one-dimensional patterns (see Figure 1) also constructed of
right riangles, and to rate the amount of
symmetry ineach of the seven patterns.Following this initial et of tasks, participants were given instruction nthe four ifferent symmetry motions?translation, re
flection,rotation, nd glide reflection?andtheircombination intothe seven classesof one-dimensional design.
Then the rating nd rankingtaskswere
readministered.We have used both ranking nd rating ests for hepreference tasks
because preferences for heseven specifickinds of symmetries inone-dimensional
bands have not been studied previouslyand thus the reliability f these measures
needs to be established. Ranking of patternswill indicate an ordering of preferences, while ratingwill further ndicate thedistances between preferences.
Task 1. Pattern Construction. Participantswere given twenty-four2 X 30 X 50mm right-angle symmetrical triangles, 12
right-sidednd 12 left-sided,ut from reen
contact-paper. They were instructed to
"make a linearpattern along a horizontal
line in hecenter of thepage using as manyof the24 trianglesas youwish. Notice that
you have 12 right-sidedand 12 left-sided
right-angletriangles that re mirror reflec
tionsofeach other.When you have finished
composing the pattern, affixthe trianglesto the page in that position by removingthe stick-on tape on theback."
Task 2. Preference Rating and Rank
ing and Amount-of-Symmetry Rating.
Participants (with heexception ofone maleart student) were shown sequentially, inrandomized order, the seven classes ofone-dimensional infinitepatterns madewith theasymmetrical right riangleseither
on a sheet of white paper 22 28 cm insize placed on the table in front f themwithpatternsize approximately 25 10 cmor on an overhead projector at the front ftheclassroom approximately threemetersfromthe participants,with the overall dimensions of thedisplay approximately 60
25 cm.
Participants were first sked to rate,then to rank each of the seven classes of
patterns intermsofpreference,
and follow
ingthis, to rateeach of the seven classesofdesign intermsof howmuch symmetrywas inthe pattern. Each task used a differentrandomized order ofpatternpresentation. Each taskwas accomplished for ll
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seven patterns before the next taskwas
undertaken. These tasks were always
given intheorder preference-rating, preference-ranking, and amount-of-symmetry
rating.All tasks used a seven point scalewith equal intervalswhere 7was the highest rating nd 1was the lowest rating.
Participantswere thengiven training nthe foursymmetrymotions and their om
binations of these fourmotions into theseven symmetry classes of one-dimen
sional infiniteatterns in heorder of translation,vertical reflection,horizontal reflec
tion,vertical and horizontal reflection om
pill
pimi
pmll
pial
Figure 1. The seven one-dimensional infinitepatterns as described inWashburn and Crowe (1988).
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bined, bifold rotation, ertical reflection ith
bifold rotation, and glide reflection as
shown inFigure 1.Trainingwas given as
follows:
The principle of symmetry isbasedon the repetitionof a fundamental
asymmetric unitbymoving it givendistance until itsuperimposes on it
self. Inthisdiagram notice how the
fundamentalpart isthe right riangleand it smoved along an imaginarylinear axis a given distance until it
superimposes upon another replicaof itself. his movement and
superposition of the part along a linear
axis can be repeated an infinite
number of times, thus the technical
term,one-dimensional infinite e
sign. There are four kinds of mo
tions thatcan move a fundamental
part inone-dimensional patterns:translation, rotation,mirror reflec
tion,and glide reflection.You have
alreadyseen themotion of transla
tion; a simple linearmovement of
the part along the axis until it u
perimposes onto thenextpartof thesame shape and size. The motionof rotation can only be two-fold
along a linear xis: two 180-degreeturnswill superimpose the part on
itself.ny other foldrotation ill take
the part offthe linear xis.The mo
tion fmirror reflection an occur in
linearbands across the horizontalaxis or across vertical axes which
perpendicularly bisect the horizon
talaxis. The motion of glide reflectionactually involvesa combination
of a horizontal reflection nd trans
lation.These fourmotions can be
combined inonlyseven ways toproduce the seven classes of one-di
mensional infinitepatterns. The
seven classes are present in thediagram you now see. [Themotions
in ach class were thendescribedas they ppear on thediagram (Figure 1)].
Class one, p111, has only themo
tionof translation.
Class two,pm11, has themotion of
vertical reflection.
Class three,p1m1, has themotionof horizontal reflection.
Class four, mm2, has the twomo
tions of vertical and horizontal re
flection.
Within and between each unit are
also points of bifold rotation.
Class five, 112, has themotion of
bifold rotation.
Class six,pma2, has themotion of
vertical reflection nd bifoldrotation.
Class seven, p1a1, has themotionof glide reflection.
The same preference ratings and preference rankings and amount-of-symmetry
ratingtasks were then repeated, butwith
differentrandomized orders of the seven
classes of one-dimensional design. For
consistency, inorder to establish the reli
ability f thepreference ratingmeasure, alltasks were administered with sequentialpresentationofpatterns.Patternswere presented simultaneously only during training.
Results
Task 1.Constructions
Examples of one-dimensional constructionsmade byartand non-artstudents areshown inFigure 2. The symmetryof theconstructed patternswas measured in wo
ways?Symmetry of theWhole Pattern and
Symmetries in the Parts of the Patternas described below. For consistency, sincesome of the participants overlapped thestick-on righttriangles in theirconstruc
tions, the symmetryof the visually apparent outline of the final formwas
recorded,regardless of theoverlap sequence. If ri
angle overlapping obscured a form, the
symmetrical relationshipso obscured wasnot recorded. Both authors rated each ofthese constructed patterns forSymmetries
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rWrV *
mo
HBBBBI
Figure 2. Examples of patterns constructed by art and non-art students from right-angle triangles.
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in he Parts of thePattern until 100% agreement was reached.
Symmetry of theWhole Pattern. Of
the three axial categories?one-dimen
sional, two-dimensional and finitepatterns?as defined byWashburn and Crowe
(1988), forty-twoarticipants created one
dimensional patterns, ten participantsmade two-dimensional patterns and none
made finitepatterns. The remaining 37
constructionswere not symmetricalwhen
considering thepatternas a whole.
Symmetries in the Parts of the Pat
terns. The presence or absence of vari
oussymmetry
motions intheparts
of the
constructions was recorded. Specifically,presence or absence of three symmetrymotions, translation,reflectionnd rotation,was noted as was presence or absence of
each of the seven one-dimensional pat
terns shown inFigure 1. The fourthmo
tion,glide reflection,was never used.
A Manova (available fromtheauthors)revealed significantmain effectsofgender,
art-training nd type of symmetrymotionin the use of the threemotions of transla
tion,mirror reflection,and rotation.The
proportions of constructions made by art
and non-art males and females that use
the three symmetrymotions are shown in
Figure 3. Inorthogonal comparisons therewere significantlymore patterns using ro
tation than translation (F(1,86)= 13.5,
< .001) and significantlymore patterns us
ingreflections than translations and rota
tions combined (F(1,86) = 28.8, p< .001).Thus, themost frequentsymmetrymotion
in he constructionswas reflection, ollowed
by rotation,then translation.These effectswere notsignificantwhen considering only
0.8
Translation Reflectionotation
SymmetryMotion
Figure 3. Proportions of constructions by art and non-art students using each of three symmetry
motions: translation, reflection and rotation.
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the constructions made bymales, eitherart students or non-art students. Females,
on the other hand,made significantlymore
constructions using reflection than other
symmetrymotions in the whole design.(Female art students; F (1,24) = 19.2,< .001 :female non-artstudents; F(1,31 )=
8.9, p<.01).
A Manova (available fromtheauthors)revealed a significantmain effectof sym
metry type and a significant interaction
between typeofsymmetry, ender and art
training. s can be seen inFigure 4, vertical reflection (pm11) and bifold rotation
(p112) were themost frequentlyused categories.
Because therewere incomplete specifichypotheses about differences between
symmetry types, non-parametric (KruskalWallis) testswere used incomparisons. In
Kruskal-Wallis tests between groups, significantly more non-art students, and non
art females inparticular, used bifold rotation in their constructions (see Figure 4)than did art students and art females in
particular (Chi-square = 5.1, p< .05; Chi
square = 5.6, < .05 respectively). It isnotable thatparticipants constructed bifold
patterns thatdid not juxtapose the right ri
angle in the same way that theywere ar
ranged inthe rating nd ranking tasks (asshown inthe seven one-dimensional patterns inFigure 1). Rather, triangleswere
grouped inpairs so that a pair together
made the outline of a rectangle.
Task 2. Rating and Ranking of Patterns
Means for art and non-art students' prefer
ence-rating, preference ranking and
0.8
111iai 112 pma2 pm11 pimimm2One-Dimensional Symmetry
Figure 4. Proportions of constructions by art and non-art students using each of the seven one
dimensional symmetry patterns.
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amount-of-symmetry-rating scores aver
aged (for implicity) cross pre-trainingnd
post-training are shown inFigure 5 also
averaged across females and males. Inan
overall Manova (available from heauthors)therewere significantdifferences between
pre-training and post-training trials
(Hotelling's Trace = .13, F (1,79)= 10.3,
< .01) and among tasks (Hotelling'sTrace = .49,F (2,78) = 38.4, p< .001), as
well as an interaction between task and
symmetry ategory (Hotelling'sTrace = 1.1,
F(2,68)= 6.3, < .001). Therefore, effects
in ach taskwere analyzed separately for
pre-trainingnd
post-trainingtrials.Means
and SDs of preference rating nd rankingand amount-of-symmetry rating for pre- and
post-training trialsare shown inTable 1.There were no significant ffectsdue to theorder ofpresentation of theseven patterns.
Preference rating. While non-art stu
dents clearly preferredpatterns generated
bycombinations ofsymmetries (pmm2an6pma2), artstudents' preferences were less
marked for ny of the symmetric patterns.(See Figure 5.) Kruskal-Wallis testswere
again used to lookat specific differences.Non-art students gave higher preference
ratings tovertical and horizontal reflection
(pmm2) than did art students both on pre
training (Chi-square= 19, p< .001) and
post-training (Chi-square = 3., p< .05) tri
als. On pre-training trialsnon-art students
gave higher ratingstovertical reflectionnd
bifoldrotationpma2)
patterns(Chi-square= 4.8, p< .05), but following trainingthere
was no longer a difference. On post-train
ingtrialsart students gave higher ratingsto translations (p111) than did non-art students (Chi-square = 5.6, p< .05).
O)?
1cceoS 3
1
ArtRatingArtRankingArtSymmetryNon-artRatingNon-artRankingNon-artSymmetry
p1111a1 p112 pma2m11
One-Dimensional Symmetry
p1m1 pmm2
Figure 5. Mean preference ratings, preference rankings, and amount-of-symmetry ratings forart and
non-art students foreach of the seven one-dimensional symmetry patterns.
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Preference ranking. Preference
rankings f translations (p111)were greaterfor rt students than fornon-art students
both before (Chi-square = 10.6, p< .001)
and after (Chi-square = 7.4, p< .01) training. Before training art students gave
higher rankingstopatternswithverticaland
horizontal reflection and bifold rotation
(pmm2) (Chi square = 9.7, < .001 ),while
following raining henon-art tudents gave
higher rankings to these pmm2 patterns
(Chi-square = 6.7, < .01).
Amount-of-symmetry-rating. Therewere no clear differences found between
art and non-art students intheirratings
of
theamount of symmetry inthe seven patterns,either before or after training. hus,while some preferences differedbetween
the groups, theirview of how much symmetrywas present inthe patterns did not
differ.
Differences between pre-training and
post-training trials. Direct comparisonswithWilcoxon summed-ranks tests between pre-and post-trainingtrials revealedincreased preferences inboth ratingsand
rankings forvertical and horizontal reflec
tionwith bifold rotation (pmm2) for ll par
ticipantsconsidered together (z= 3.2, <
.001; = -2.3, < .05). (Allzs reportedhere are two-tailed). Ratings for mount
of-symmetry increased following trainingfortranslation
(p111),horizontal reflection
(p1m1), bifold rotation (p112) and glide re
flection(p1a1)(z= -3.25, < .001 ; = 2.1,< .05;
=-2.5, < .05;
=3.5, < .001
Table 1.Mean Ratings and Rankings ofSeven One-Dimensional Patterns Pre- and
Post-Training.
Preference Ratings
p111 p1a1 p112 pma2 pm11 p1m1 pmm2
Pre-trainingArt
Non-art
Post-trainingArtNon-art
3.192.82
3.38
2.53
4.29
4.51
4.5
4.5
4.284.79
4.595.87
3.824.61
4.41
4.42
3.37
3.92
3.82
3.87
4
4.47
4.64
4.32
3.674.32
5.29
5.63
Preference Rankingsp111 piai p112 pma2 pm11 p1m1 pmm2
Pre-training
ArtNon-art
Post-trainingArt
Non-art
2.91
1.77
2.531.66
4.2
4.32
4.38
3.76
4.73
4.42
4.47
4.84
4.72
4.61
4.784.45
3.16
3.5
3.3
3.29
4.083.79
4.32
4.2
3.97
5.44
4.495.79
Amount-of-SymmetryRatings
p111 p1a1 p112 pma2 pm11 p1m1 pmm2
Pre-training
ArtNon-art
Post-trainingArtNon-art
2.832.92
3.993.84
3.823.5
5
4.18
4.24.73
5.11
4.94
5.14.76
5.44
5.08
5.254.93
5.545.29
5.425.29
5.88
5.63
6.576.27
6.42
6.24
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respectively).Thus, while preferenceswere
increased by trainingforthemost detect
able (Royer, 1981) and perhaps most
salient symmetry type of the seven one
dimensional patterns (pmm2),amount-of
symmetry ratings increased for the less
salient types of symmetry.
Discussion
The prevalent use of reflections incon
structions,particularly y females, appearstomirror the prevailing use of reflectionsindrawings by untrained children andadults (Humphrey, 1997). The obvious sa
lience of mirror reflectionscan be seen inthe present study inproductions made byboth trained and untrained participants.The use of bifold rotations, less preferredsymmetry, y untrainedparticipantscan be
explained by thesalience of reflective ymmetries. That is,most of theexamples with
bifold symmetry took the formof two tri
angles juxtaposed such thattheir ommon
outline produced a rectangular form(See
Figure 2 forexamples) itself shape withvertical reflection.Thus, the end result of
using bifoldmotion to construct a patternis shape with themost salient symmetry,vertical reflection.
A critical finding f this research is thatartists and non-artists did not choose thesame symmetries in isual preference tasksas theydid inproduction tasks. The participants untrained in rt showed clear preference in
ratingsas well as in
rankingsfor
patternswith pmm2 symmetry.This symmetry produces a stable shape with dominant mirror reflections. Ithas also beenshown tobe easily detected (Royer, 1981 ).In ontrast, art students preferred patterns
withmore motion, such as those generatedby rotation. hus, theyratedp112the highest and ranked pma2 the highest. The
pmm2 patternwas notamong themost preferredbyartstudents.Although thispattern
has bifold symmetry,the prevailing visualeffectemphasizes vertical and horizontal
(p111) and horizontal reflection(p1m1).For themost salient symmetry,vertical
reflection (pm11), our results agree with
those ofRentschier et. al. (1999). Neither
preferences norperception ofpm11 (vertical reflection) ppear tochange with train
ing for either art students or the control
group. However, whenwe
trained respondents on theof/iersymmetries,training edto increased preference for hepmm2 patterns forboth the art and non-art respondents, although ratingsof amount-of-symmetry did not increase forthispattern fol
lowing training. entschler et. al.were alsoable to influencepreferences for "repetition" (p111) patternswith theircategorization task. Inour study, symmetryclasses
p111, p1m1, p112 and p1a1 showed in
creased ratings of amount of symmetry
followingtraining.Apparently participantsgained an appreciation that different ymmetries existed and thatdifferent ymmetriescould yield different atterns.
While therewere specific differences
between rating nd rankingof some patterns, overall the general trends of ratingand rankingwere remarkably similar, ascan be seen inFigure 5. Perhaps simulta
neous, ratherthansequential presentationof thepatternswould yielddifferent esults,
particularly in rankingtask. The mannerof presentation could be reconsidered infutureresearch.
In summary, while the perception of
symmetry, as indicated in the relative
amount-of-symmetry ratings,did notdifferbetween artstudents and non-artstudents,therewere significant differences in the
productionof
symmetrical patternsand in
the preferences fordifferentsymmetriesbetween artand non-art individuals.Additional training in symmetries producedawareness for he less detectable symmetries,such as translationand glide reflection.
Our results confirmthat there isa general special salience formirror reflection,and, in ddition, show how one kindof culturalexperience (artistic ctivity) provides
an overlay that leads to specific preferences forspecific symmetrical arrangements. These results suggest thatmuchmore work needs tobe done toclarifyhowdifferent spects of culture affectpercep
One-Dimensional Patterns 67
7/29/2019 Washburn, Humphrey. 2001. Symmetries in the Mind Production , Perception , And Preference for Seven One-Dim…
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tuai preferences for nd production of dif
ferentsymmetries. Our futureworkwill fo
cus on developing a cross-cultural test to
better study the factors related to these
cultural preferences.
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Dorothy Washburn
120 Pleasant Valley Road
Titusville, NJ 08560
Diane Humphrey
Kings College
Departmentof
Psychology266 EpworthAvenue
London, Ontario, Canada
N6A2M3
68 DorothyWashburn / iane Humphrey