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,
natural patterns have been produced by simple mathematical equations
solutions appear unpredictable (chaotic). Yet the simplicity and
of the equations ensure a degree of order in the resulting patterns.
first experiment shows how aesthetic preferences correlate with the
dimension (F) and the Lyapunov exponent (L) of the
F reflects the extent that space is filled and L
the unpredictability of the dynamical process that produced the
Results showed that preferred patterns had an average F = 1.26
an average L = 0.37 bits per iteration, corresponding to many
objects. The second experiment is a preliminary test of individual
in preferences. Results suggest that self-reported creative individuals
have a marginally greater preference for high F patterns and
scientific individuals preferred high L patterns. Objective
suggest that creative individuals had a slightly greater preference for
patterns with a low F.
Ref: D. J. Aks
J. C. Sprott, Empirical Studies of the Arts 14,
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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
Fig. 2. Summary of preferences in the F-L plane for two
subjects; (a) HR prefers low F and high L; (b) DA
high F and lower L.