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Reduction of Physiological Stress Using Fractal Art and Architecture

Taylor, R. P.

Leonardo, Volume 39, Number 3, June 2006, pp. 245-251 (Article)

Published by The MIT Press

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In art school I was told that Monets water liliescalm the observer, while van Goghs sunflowers electrify. Towhat extent, however, do paintings really affect the observersphysical condition? The foundations of this question date backto 1890, when the connection between psychological statesand physiological states was first considered [1]. However, the

health trends of modern societycause this question to take on newurgency.

Stress is woven deep into our dailyexperiences. One in four people in the U.S.A. suffers from stress, and the associated annual cost to so-ciety is estimated to be $300 billion[2]. Consequently, researchers aresearching for effective ways to re-duce stress. One hope lies in adapt-ing the interior and exterior ofbuildings to create environmentsthat are more in tune with physi-ological responses to visual stimuli.Such projects offer the potential for interdisciplinary collab-orations among scientists, artists and architects.

There are several characteristics of artworks that might beengineered to induce a desirable physiological response. Theseinclude subject matter, color and compositional form. I willfocus on the latter characteristic. Furthermore, given the prev-alence of natural landscapes in art and the popularity of windows that offer views of natures scenery, a useful startingpoint lies in the investigation of art composed from naturespatterns.

For this reason, I will focus on fractal patterns. A diverserange of natural objects are fractal, including mountains,clouds, rivers and trees [3,4]. Furthermore, computers haveled to the popularity of mathematically generated fractals. Frac-tals have also assumed a rapidly expanding role as an art form.This has been emphasized by my own discovery of fractal pat-terns in the works of Jackson Pollock [5,6].

Owing to fractals growing impact on cultures around theworld and their prevalence in nature, they constitute a centralfeature of our daily visual experiences. How, then, do we re-spond to their visual characteristics? In this article, I addressthis issue by analyzing the results of an experiment performedby the National Aeronautics and Space Administration(NASA), in which skin conductance measurements were usedto measure peoples physiological responses to natural images[7,8]. My fractal analysis of these images provides a prelimi-nary demonstration that certain forms of fractal patterns mightbe used to reduce physiological stress.

Over the past 30 years, the visual appeal of fractals has beencelebrated frequently [912], culminating in the dramaticidentification of them as the new aesthetic [13]. The dis-

2006 ISAST LEONARDO, Vol. 39, No. 3, pp. 245251, 2006 245

Reduction of Physiological Stress Using Fractal Art and Architecture

R.P. Taylor

R.P. Taylor (physicist and art theorist), Physics Department, University of Oregon, Eugene,OR 97403, U.S.A. E-mail: .

A B S T R A C T

The author reviews visualperception studies showing that fractal patterns possess anaesthetic quality based on theirvisual complexity. Specifically,people display an aestheticpreference for patterns with mid-range fractal dimensions,irrespective of the method usedto generate them. The authorbuilds upon these studies bypresenting preliminary researchindicating that mid-range fractalsalso affect the observersphysiological condition. Thepotential for incorporating thesefractals into art and architectureas a novel approach to reducingstress is also discussed.

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Fig. 1. A photograph of a forest (top); an artistic rendition of alandscape (middle); and painted lines (bottom). ( Richard Taylor)

Derek Youngmuse_logo

covery that this aesthetic quality might be accompanied by a positive response in the observers physiology lends con-siderable support to previous proposals for fractal art and fractal architecture[1418]. I therefore consider the artisticand architectural challenges of incorpo-rating fractal imagery into buildings toaffect peoples perceptual and physio-logical responses.

STRESS MEASUREMENTMeasurement of an observers skin con-ductance might appear to be an unusualtool for judging peoples responses to art.However, electro-dermal measurementsare a well-established method for quan-tifying changes in an observers physiol-ogy [19]. In a 1986 NASA study, JamesWise used skin-conductance measure-ments to investigate the physiological ef-fects of observing art [20]. The three

during periods of induced stress and de-creased during the low-stress periods. Forexample, Fig. 2 shows the rise and fallmeasured over the work-rest sequence for participants continuously exposed tothe control image. The procedure for thegeneration of this plot is presented in de-tail elsewhere [22]. Significantly, ananalysis of the 24 participants responsesrevealed that the change in conductanceG between work and rest periods de-pended on which image was observed.For the artificial pattern (Fig. 1, bottomimage), G was 13% greater than for thecontrol image, indicating that the arti-ficial pattern increased the physiologi-cal response to stress. In contrast, the G values for the natural images were3% (top image) and 44% (middle image)lower than for the control [23]: These im-ages dampened the physiological responseto stressful work.

These intriguing results indicate thepotential for the use of art to influencepeoples physiological condition, in par-ticular stress. The fact that the two art-works featuring natural images (the topand middle images) delivered a positiveimpact on the observers physiology isconsistent with earlier research in envi-ronmental psychology that explored thephysiological health benefits of usingwindow views of natural environments[24]. The results also support findings inlandscape architecture research demon-strating peoples preference for naturallandscapes [25]. However, based on theseearlier investigations, the top rather thanthe middle image is expected to be mosteffective, because it is an accurate pho-tograph rather than an artistic renditionof a natural scene. What visual charac-teristic of this rendition triggered such adramatic impact on the participants? Toanswer this crucial question, it is neces-sary to explore the aesthetic qualities ofnatural scenery in greater depth.

FRACTAL AESTHETICSAt the time of the experiment, the tradi-tional studies of perceptual and environ-mental psychology assessed the aestheticsof nature using vague qualities such asthe degree of naturalness of the scene[26] or the dominance of selected topo-logical features such as water or hills [27].No unified theory existed to describe thevisual information that determines aes-thetic responses to natural scenery. In-stead, theories were limited to discussionsconcerning optimal amounts of balancebetween order and disorder [28] andsimplicity and complexity [29]. Otherstudies overlooked the subtle complexity

artworks used, each measuring 1 2 m,are shown in Fig. 1: a photograph of a for-est (top), an artistic reproduction of asavannah landscape (middle) and an ab-stract pattern (bottom). An additionalwhite panel served as a control.

Participants were seated one at a timein a room facing one of the four images.During continuous exposure to an im-age, each participant performed a se-quence of three types of mental tasksdesigned to induce physiological stress(arithmetic, logical problem-solving andcreative thinking). Task periods were sep-arated by 1-minute recovery periods, thuscreating a sequence of alternating high-and low-stress periods. To measure theparticipants physiological responses tothe stress induced by mental work, skinconductance was monitored continu-ously during this sequence.

Consistent with previous skin-conduc-tance studies [21], conductance peaked

246 Taylor, Reduction of Stress Using Fractal Art

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NFig. 2. The conductance changeduring the task sequence (blacksquares indicate rest periods) forparticipants who were continu-ously exposed to the controlimage. ( Richard Taylor) Theprocedure for generating thisplot was as follows: First, toestablish a common conductancescale for these participants, eachparticipants conductance wastransformed to Z-scores. Then,for each task in the sequence,these Z scores were averagedacross participants. This mean Zconductance was then plotted forthe whole sequence of tasks [75].

Fig. 3. (a) Fractal tree patterns repeating at different magnifications. (b) Patterns and their Dvalues. ( Richard Taylor)Top row, left to right: a smooth line (D = 1), two fractal poured paintings (D = 1.1 and 1.9)and a filled area (D = 2). Bottom row, left to right: the horizon line (D = 1), clouds (D = 1.3),a forest (D = 1.9) and a filled area (D = 2).

of natures patterns and focused on sim-plified representations based on Euclid-ean shapes [30].

An important step in the understand-ing of natures visual characteristicsoccurred when Benoit Mandelbrot em-phasized that the complexities and ap-parent irregularities of natures organicpatterns could not be modeled using Eu-clidean geometry [31]. Instead, manynatural objects belong to fractal geome-try, consisting of patterns that recur at increasingly fine magnifications (see, forexample, the fractal tree in Fig. 3a). Frac-tal patterns visual characteristics neces-sitate the use of descriptive approachesthat are radically different from those ofEuclidean geometry. The fractal dimen-sion D is a central parameter and quan-tifies the fractal scaling relationshipbetween the patterns observed at differ-ent magnifications [32]. For Euclideanshapes, dimension is a familiar conceptdescribed by integer valuesa smoothline has a D value of 1, whereas a com-pletely filled area has a value of 2. For therepeating patterns of a fractal line, D liesbetween 1 and 2. Figure 3b demonstrateshow a fractals D value has a profound ef-fect on its appearance.

Although the term fractal was intro-duced in the 1970s, it was not until the1990s (long after Wises experiment) thatvisual perception experiments focusedon fractal aesthetics [33]. In one of the

to 1.5. Figure 3 shows examples of frac-tals that lie within and outside this range.The universal character of fractal aes-thetics was further emphasized by a re-cent investigation showing that genderand cultural background of participantsdid not significantly influence this D pref-erence [40].

Significantly, prevalent patterns in na-ture have D values in this range (for ex-ample, clouds and coastlines), raising the possibility that the eye is aestheticallytuned to the fractals surrounding us innature. In light of this speculation, we ex-tended our studies to consider aestheticpreferences for natural scenes [41]. Ourprevious experiments had focused onsimple natural images featuring just oneform of fractal (for example, the cloudsor trees shown in Fig. 3). In contrast, typ-ical natural scenes are composed of arange of fractal objects. Although thecharacteristics of typical scenes are there-fore quite complex, their fractal statisticsare well charted [42]. How, then, doesthe preference for mid-range D values ofsimple fractal objects [43] extend tothese visually intricate fractal scenes?

Owing to a typical scenes complexity,it is necessary to select a dominant char-acteristic of the scene and examine itsimpact in detail. Research indicates thatedge contours play a dominant role indefining perception of fractals [44]. Theimportance of edge contours is sup-

first such experiments, performed in1994, I used a chaotic pendulum [34] to generate fractal and non-fractal pat-terns. In perception experiments basedon these images, 95% of participants preferred the fractal to the non-fractalpatterns [35]. Figure 4 shows two of thepatterns used. Given the impact of D on the appearance of fractals, do ob-servers base aesthetic preference on D?Pioneering studies by Clint Sprott andDeborah Aks conducted from 1993 to1996 used computer-generated fractalimages and revealed a preferred D valueof 1.3 [36].

In 1999, my discovery that Pollockspaintings are fractal [37] reinvigoratedinterest in fractal aesthetics. My analysisrevealed that the D values of Pollockspaintings evolved during the period 19431952 in the direction of aesthetic relianceon D [38]. Collaborating with BrankaSpehar, Ben Newell and Colin Clifford, Iperformed aesthetic-preference experi-ments incorporating three categories offractals: photographs of natural objects,computer-generated images and Pollockpaintings. Our results showed that thepreference for mid-range D values re-vealed by Sprotts computer-generatedfractals was universal in the sense thatthis preference extended to fractal im-agery found in nature and art [39]. Fora wide variety of fractals, visual appealpeaks for the mid-range D values of 1.3

Taylor, Reduction of Stress Using Fractal Art 247

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Fig. 4. The chaotic pendulum (left) employed to generate non-fractal (top right) and fractal (bottom right) poured paintings. ( Richard Taylor)

ported by eye-tracking experimentsthat monitor direction of gaze. These ex-periments show that the eye fixates pre-dominantly on edges when examining a scene [45]. Therefore, a promising approach to investigating a fractal sceneis to select a prominent edge and de-termine its aesthetic impact. The sky-line forms the dominant contour in many scenes, with the D value depend-ing on the objects that define the con-tour [46]. I collaborated with CarolineHagerhall and Terry Purcell in prefer-ence experiments showing that the mostpreferred scenes had fractal skylines witha D value of 1.3 [47]. Figure 5 shows atypical natural scene and the skylinesfractal contour. The results offer a cleardemonstration that the preference formid-range D values revealed for sim-ple fractal shapes extends to the fractalcharacteristics of more intricate fractalscenery.

FRACTAL STRESS REDUCTIONDoes this appreciation for mid-D values(1.31.5) explain the physiological re-sponse induced by the middle image of

lished by the combination of the edgecontours of all the objects in the image.This approach has met with success inprevious investigations of fractals foundin art and nature [49].

To perform the fractal analysis of theedge pattern, I employed the box-count-ing method, in which the pattern is cov-ered with a mesh of identical squares[50]. The patterns statistical scaling qual-ities are then determined by calculatingthe proportion of squares occupied bythe pattern. This process is repeated forincreasingly fine meshes. Reducing thesquare size is equivalent to looking at thepattern at finer magnification. In this way,the patterns statistical qualities can becompared at different magnifications.Specifically, the number of squares, N(L),that contain part of the pattern arecounted, and this is repeated as the size,L, of the squares is reduced. For fractalbehavior, N(L) scales according to the re-lationship N(L) ~ L

D, where D lies be-

tween 1 and 2 [51]. The D values, whichchart the scale invariance, were extractedfrom the gradient of a graph of log N(L)plotted against log L.

Using this analysis, the artificial pat-tern (Fig. 1, bottom image) was foundnot to be fractal, while the forest pho-tograph (top image) and artwork of the natural scene (middle image) werefractal, with D values of 1.6 and 1.4, re-spectively. Significantly, this result is con-sistent with the above investigations of peoples visual perception of fractals.The savannah scene, which provided thegreatest dampening of physiological re-sponse, has a D value that falls into theaesthetically pleasing range, while theforest D value falls outside this range.

Fig. 1? To answer this, I collaborated withTed Martin and James Wise to analyze theart featured in the original NASA exper-iment. Adopting the edge analysis tech-niques discussed above [48], I performeda fractal analysis on the pattern estab-


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Fig. 5. A photograph of a natural scene (top) used in preference experiments, along with theextracted skyline contour (bottom). (Photo Caroline Hagerhall)

Fig. 6. The Sydney Opera House, designed by Jorn Utzon. ( Richard Taylor)

IMPLICATIONS FOR FRACTALART AND ARCHITECTUREThese results suggest that the observersphysiological condition might be influ-enced positively by mid-D fractals. It isimportant to emphasize the preliminarynature of the results, which are based ononly four images. In particular, D is justone of a number of visual characteristicsthat vary between the images. However,within this context, it is informative to re-turn to the universal quality of fractalaesthetics identified in the perception ex-perimentsdespite the diverse visualproperties of the images used (naturalobjects and scenes, paintings and com-puter patterns), D was found to be a sig-nificant factor for determining aestheticpreference.

An appealing consequence of thiswork lies in the rich variety of images thatmight be used for dampening physiolog-ical response to stress. Whereas previousproposals for stress reduction concen-trated on natural images [52], our resultsemphasize that natural scenery repre-sents a small subset of the fractal imagesthat might be effective in stress reduc-tion. These include computer-generatedfractals and abstract paintings. For ex-ample, Sprott has previously advocatedthe use of computers for generating arich variety of fractals [53]. Furthermore,my own research has demonstrated theease with which a chaotic pendulum cre-ates paintings where the fractal contentcan be tuned [54]. These approachescould be used to produce a library of frac-tal images to be used to improve peoplesphysiological condition.

Our investigations of fractal skylines

Is it practical to create buildings witha fractal appearance? One approach is toconstruct the buildings framework basedon fractal geometry. A less radical ap-proach is to use a Euclidean shape for the buildings basic structure and in-corporate fractals into the design using, for example, paint, lighting or attachedstructures. Regardless of the approach,the challenge, of course, lies in the abil-ity to repeat the patterning process at dif-ferent scales. However, this challenge maynot be as difficult as it seems.

One practical consideration concernsthe magnification range over which thepatterns must follow fractal behavior inorder to induce the desired physiologi-cal response. Whereas mathematical frac-tals extend from the infinitely large to theinfinitesimally small, physical fractals(generated by nature and artists) are lim-ited to a finite magnification range. ForPollocks paintings, fractal behavior ischarted from the finest speck of paint up to the canvas size, representing a mag-nification range of 1,000 [57]. For thenatural scenery, the skyline D value wasobserved over a factor of 250 [58].

However, these large observationranges are unusual for physical fractalstypically, the smallest pattern is only 25times smaller than the largest [59]. Mo-tivated by this fact, the images used in ourperception experiments were displayedsuch that the smallest resolvable patternwas approximately 25 times smaller thanthe largest [60]. This limited magnifica-tion range was sufficient to induce the Dpreferences discussed above. Therefore,fractal architecture can effectively be lim-ited to patterns spanning a magnificationrange of 25.

Other crucial factors also demonstratethat response-based fractal architectureis an achievable proposition. First, ourperception results indicate that relativelysimple (mid-D) fractals are sufficient toinduce a preference. This is highlightedby the images shown in Fig. 3the intri-cate, rich structure found in high-D frac-tals would be a much greater challengethan the relatively simple structure oflow-D fractals. Secondly, traditional ar-chitectural studies demonstrate that fa-ade complexity influences aestheticpreference significantly less than com-plexity in the buildings skyline [61]. Thisindicates that research should be di-rected at establishing fractal skylines ofbuildings instead of the more involvedstrategies that would be required to es-tablish fractal texture across faades.Thirdly, recent preference studies showthat it is not necessary to match a build-ings fractal skyline to background frac-

[55] indicate that stress-reducing imagesneed not be restricted to simple fractalpatterns. The presence of a mid-rangefractal contour buried within a scene issufficient to affect the aesthetics. Thus itshould be possible to use paintings de-picting people and buildings and to addthe fractal content into the backgroundcontours of the scene. This prospect addsto the variety of potential images, andalso presents the opportunity to combinefractal patterning with other stress-re-ducing factors such as the paintings sub-ject matter and color.

Not all fractal art will be suitable fordampening physiological responses tostress, however. An important conse-quence of the above research is thedemonstration that, contrary to the pre-vious proposals of using window viewsand photographs of natural scenes, nat-uralness of the image is not sufficient to produce the desired effect. The effec-tiveness will depend on the images spe-cific D value. For example, the fractallandscape of Fig. 1 (top) produced a rel-atively mild dampening despite being anaccurate photographic depiction of a nat-ural scene.

The concept of fractal architecturebuilds on earlier proposals of biophiliaand the drive to incorporate nature intourban landscapes [56]. However, theseearlier strategies are often impractical for cities, where building density limitsexposure to nature. Furthermore, theresearch presented here shows that nat-uralness is not enough to induce physio-logical responsesspecific D values arerequired. Thus, it is necessary to designbuildings fractal geometry to feature spe-cific D values.


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Fig. 7. The repeating patterns of the Borobodur Temple. ( Richard Taylor)

tal scenery [62], limiting contextual con-cerns. In particular, the fractal skylinedoes not have to be matched to fractalcloud patterns, thus excluding the highlyunfeasible prospect of having to matchthe fractal designs of buildings to preva-lent weather conditions.

Finally, perhaps the most importantpractical consideration to be researchedconcerns the degree to which shapes can deviate from fractal behavior and stillinduce the desired response. For exam-ple, although the Sydney Opera House,shown in Fig. 6, is not strictly fractal, thepattern created by simple shapes at sev-eral sizes might be sufficient to mimicfractals and induce the desired physio-logical response. If future investigationsshow this to be the case, this relaxa-tion of practical conditions will makefractal architecture a highly realisticproposition.

CONCLUSIONSAlthough preliminary, the results dis-cussed above have enormous potentialthe motivation of this article is there-fore to trigger further investigations. Inparticular, it is important to extend the physiological measurements beyondelectro-dermal responses to include car-diovascular, eye-tracking and pupillog-raphy responses. In addition, future experiments should narrow the precisefractal character of the patterns that max-imize the responses by considering addi-tional parameters such as lacunarity andthe full spectrum of dimensions obtainedfrom a multi-fractal analysis [63].

These experiments could provide a fas-cinating insight into the impact that frac-tal art and architecture might have on anobservers perceptual and physiologicalresponses. Stress reduction is of enor-mous benefit to society, and this novel approach of using fractals might proveparticularly useful for therapeutic envi-ronments such as hospitals or in situ-ations where people are deprived ofnatures fractalsfor example, in win-dowless rooms or research stations in theAntarctic and in outer space. NASAs mo-tivation for conducting the experimentswas to explore methods of maintaininglow stress for astronauts, an aim that hasbecome topical with the recent calls formanned missions to Mars.

The challenges of incorporating frac-tals into the interiors and exteriors ofbuildings will require an interplay be-tween scientific, artistic and social con-siderations. In particular, the manner inwhich people are exposed to the patternsshould be unobtrusive. Certainly, a future

Pollocks early poured paintings (19431944) [73] and Lloyd Wrights PalmerHouse (1950) [74].

Acknowledgments

The Research Corporation, the National ScienceFoundation and the Addario Foundation are ac-knowledged for financial support.

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Could a common set of fractal imagesbe used for everyone? Although the ma-jority of participants in the perceptionexperiments preferred mid-range fractals[65], there is some evidence that creativepeople prefer the greater complexity ofhigh-D patterns [66], raising the questionof whether fractal images will have to betuned to individual preferences. Fur-thermore, to prevent saturation of the re-laxation effect, the fractal images wouldhave to be varied over time, perhapsthrough the use of electronic screens orevolving lighting conditions. If thesechallenges seem daunting, it is worthstressing that we may already be using this approach to stress reduction withoutknowing it. Take, for example, staringinto the flickering flames of a fire or look-ing up at tree branches swaying in thewind. The patterns in both cases varywith time while preserving their fractalqualities. The combination of their frac-tal content, along with other factors suchas color and subjective associations, al-most certainly reduce our stress.

The prevalence of artificial fractals sug-gests the possibility that we have beenmaking use of fractal stress reductionthroughout history. We expect our find-ings to apply to a range of fractal patternsappearing in art, architecture and ar-chaeology, spanning five centuries! Oneexample, shown in Fig. 7, is the skyline ofthe temple of Borobodur built in Javaduring the 8th century. Other examplesinclude the Nasca lines in Peru (pre7thcentury) [67], Gothic cathedrals (12thcentury) [68], the Ryoanji Rock Gardenin Japan (15th century) [69], Leonardossketch The Deluge (1500) [70], Hokusaiswoodcut print The Great Wave (1846)[71], Eiffels tower in Paris (1889) [72],


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Manuscript received 2 December 2004.

Richard Taylor is an associate professor ofphysics, psychology and art at the Universityof Oregon. His interdisciplinary research intofractals, chaos and complexity ranges fromnano-electronics to the human visual system.

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