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Abstract

Complexity has stood out as an important predictor of aesthetic value judgments since the earliest days of empirical aesthetics. However, there is a considerable lack of consensus on the best way to formalise complexity. Moreover, a large fraction of previous studies used handcrafted stimuli and measures, which compromises the reproducibility and generalisability of results. To overcome these obstacles, we used controlled computer-generated visual patterns and computational complexity measures to model subjective complexity evaluations. We used cellular automata to generate diverse 2D black-and-white pixel-grid patterns (n=240) that are structurally reproducible. We collected complexity ratings from 80 participants for these patterns. We programmatically computed objective complexity measures such as density, entropy (Shannon entropy averaged over multiple scales), spatial complexity (mean information gain over pairs of pixels), Kolmogorov complexity (length of shortest computer program to produce the desired pattern), and local and global asymmetry. We also introduced an “intricacy” measure that quantifies the number of components in the pattern using a graph-based approach. Linear mixed effects regression indicated that a weighted combination of spatial complexity and intricacy was an effective predictor (R^2test = 0.44) of subjective complexity ratings. This implies that people’s complexity judgments depend on the number of distinct visual elements in the pattern along with their local spatial distribution. Contrary to popular belief, neither symmetry nor entropy related to subjective complexity. An extension of our experiment on 60 participants tested for generalisation and showed that the combination of spatial complexity and intricacy consistently predicted complexity ratings both for larger patterns and for patterns with an additional grey colour. This work introduces stimuli and measures that offer an opportunity for systematic computational investigation of the relationship between subjective and objective complexity and develops a complexity metric that can be widely used to predict subjective complexity evaluations of visual objects.