Quantifying Aesthetic Preference for Chaotic Patterns

Deborah J. Aks
University of Wisconsin at Whitewater


Julien C. Sprott
University of Wisconsin at Madison


Art and nature provide much of their aesthetic appeal from a balance of simplicity and complexity, and order and unpredictability. Recently, complex natural patterns have been produced by simple mathematical equations whose solutions appear unpredictable (chaotic). Yet the simplicity and determinism of the equations ensure a degree of order in the resulting patterns. The first experiment shows how aesthetic preferences correlate with the fractal dimension (F) and the Lyapunov exponent (L) of the patterns. F reflects the extent that space is filled and L represents the unpredictability of the dynamical process that produced the pattern. Results showed that preferred patterns had an average F = 1.26 and an average L = 0.37 bits per iteration, corresponding to many natural objects. The second experiment is a preliminary test of individual differences in preferences. Results suggest that self-reported creative individuals have a marginally greater preference for high F patterns and self-reported scientific individuals preferred high L patterns. Objective tests suggest that creative individuals had a slightly greater preference for patterns with a low F.

Ref: D. J. Aks and J. C. Sprott, Empirical Studies of the Arts 14, 1-16 (1996)

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Fig. 1. Sample screen display as exhibited to subjects showing four typical attractors. Top row has L near zero; bottom row has L near 0.2. Left column has F about 1.1; right column has F about 1.3.
[Figure 1]

Fig. 2. Summary of preferences in the F-L plane for two typical subjects; (a) HR prefers low F and high L; (b) DA prefers high F and lower L.
[Figure 2a](a)

[Figure 2b](b)