Aesthetic Responses to Exact Fractals Driven by Physical Complexity - Bies, Alexander J.; Blanc-Goldhammer, Daryn R.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E. (Frontiers in Human Neuroscience, 2016)
Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality (D), symmetry, recursion, and the number of segments in the generator using a variety of fractal patterns. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as D increases. For the majority of individuals, preference increased with D. We replicated these results in a second study, while also testing the effects of symmetry and recursion by presenting fractals without mirror symmetry (asymmetric dragon fractals and radially symmetric dragon fractals) and fractals with mirror symmetry (Sierpinski carpets and Koch snowflakes). We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in asymmetric patterns, while others were less discriminating. Here, what distinguished among respondents was their sensitivity to the presence of mirror symmetry. All participants in the second study exhibited a general increase of preference with D. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a pattern. Conceptualizations such as Berlyne’s (1971) and Redies’ (2015) theories of aesthetics provide a suitable framework for interpretation of our data with respect to the individual differences that we detect. Future studies that incorporate physiological methods to measure the human aesthetic response to exact fractal patterns would further elucidate our responses to such timeless patterns.