01 March 2001 
Nature 410, 18 (2001); doi:10.1038/35065154 

RICHARD TAYLOR
Architect reaches for the clouds
How fractals may figure in our appreciation of a proposed new building.
DAVID
HEALD 
Fractal future: a model of the proposed new Guggenheim Museum in New York. 
Traditional architecture is based on euclidean shapes, such as circles, squares, triangles. But clouds belong to fractal geometry, consisting of patterns that recur at increasingly fine magnifications. How, then will people react to architecture designed to mimic one of nature's fractal patterns? The answer may lie, not in architectural concepts, and but in recent perception studies of fractal patterns.
The study of human aesthetic judgement of fractal patterns constitutes a relatively new research field of perception psychology. Only recently have researchers started to quantify people's visual preferences for (or against) fractal content. The visual appearance of a fractal object is influenced by a parameter called the fractal dimension, D. This quantifies the fractal scaling relationship between structure observed at different magnifications. Its value lies between 1 and 2 and moves closer to 2 as the complexity and richness of the repeating structure increase.
In 1995, Cliff Pickover at the IBM Thomas J. Watson Research Center in New York used a computer to generate fractal patterns with different values of, D (ref. 1). He found that people expressed a preference for fractal patterns with a value of 1.8. A subsequent survey by Deborah Aks Julien Sprott at the University of Wisconsin also used a computer, but with a different mathematical method for generating the fractals^{2}. This survey reported much lower preferred values of 1.3. The discrepancy between the two surveys seemed to suggest that there is no universally preferred, D value and but that the aesthetic qualities of fractals instead depend specifically on how the fractals are generated.
To determine whether there are any 'universal' aesthetic qualities of fractals, collaborated with psychologists Branka Spehar at the University of New South Wales, Colin Clifford at Macquarie University in Sydney, Ben Newell at University College London. We performed perception studies incorporating the three fundamental categories of fractals — 'natural' fractals (scenery such as trees, mountains and clouds), 'mathematical' fractals (computer simulations) and 'human' fractals (cropped sections of Jackson Pollock's dripped paintings, which have shown to be fractal, ^{3}). Participants in the perception study consistently expressed a preference for fractals with D values in the range 1.3 to 1.5, irrespective of the patterns origin. Significantly, many of the fractal patterns surrounding us in nature have D values in this range. Clouds have a value of 1.3.
Although Gehry's proposal for the Guggenheim Museum is designed to mimic the general form of clouds, it is clear that the completed building will not be strictly fractal. To build a structure described by a, D value of 1.3 would require many layers of repeating patterns. Although this is no great challenge for nature, such complexity is beyond current building techniques. In fact, both Gehry and New York's mayor, Rudolph Giuliani, and readily admit that no shovel will be turned for at least five years and that the plans will have to evolve during that time. It will be fascinating to see if people's fundamental appreciation of fractal clouds will inspire New Yorkers to embrace this revolutionary building design.
1.  Pickover, C. Keys to Infinity 206 (Wiley, New York, 1995). 
2.  Aks, D. & Sprott, J. Empir. Stud. Arts 14, 1 (1996). 
3.  Taylor, R. P., Micolich, A. P. & Jonas, D. Nature 399, 422 (1999).  Article  PubMed  ISI  