Beauty and structural complexity

We revisit the long-standing question of the relation between image appreciation and its statistical properties. We generate two different sets of random images well distributed along three measures of entropic complexity. We run a large-scale survey in which people are asked to sort the images by preference, which reveals maximum appreciation at intermediate entropic complexity. We show that the algorithmic complexity of the coarse-grained images, expected to capture structural complexity while abstracting from high frequency noise, is a good predictor of preferences. Our analysis suggests that there might exist some universal quantitative criteria for aesthetic judgment.

Figure 1

(a) Fourier magnitude-generated images, and (b) box-counting-generated images, both series with increasing complexity from left to right. These images were used for our large-scale survey.

Figure 2

Results of the two different surveys (Zooniverse: solid black line; Mechanical Turk: dash-dotted gray line). The red diamonds markers indicate the structural complexity ${\tau }_{\mathrm{cg}}$ defined below. We rescaled and shifted vertically ${\tau }_{\mathrm{cg}}$ to show that the maximum scores also correspond to maximum structural complexity. The blue circles reflect the complexity measure proposed in Ref. [35]. Top: Image series of Fig. 1. Bottom: Image series of Fig. 1. Error bars reflect the 95% confidence interval using the bootstrap method [36].

Figure 3

Illustration of the coarse-graining procedure on images a1, a4, and a6, with $r_{\mathrm{cg}}=7$ and $\delta =0.23$.