Fractal curves and complexity

Abstract

Fractal curves were generated on square initiators and rated in terms of complexity by eight viewers. The stimuli differed in fractional dimension, recursion, and number of segments in their generators. Across six stimulus sets, recursion accounted for most of the variance in complexity judgments, but among stimuli with the most recursive depth, fractal dimension was a respectable predictor. Six variables from previous psychophysical literature known to effect complexity judgments were compared with these fractal variables: symmetry, moments of spatial distribution, angular variance, number of sides,P2A, and Leeuwenberg codes. The latter three provided reliable predictive value and were highly correlated with recursive depth, fractal dimension, and number of segments in the generator, respectively. Thus, the measures from the previous literature and those of fractal parameters provide equal predictive value in judgments of these stimuli.