The complexity of images critically influences our assessment of their beauty. However, studies relating assessments of complexity and beauty to potential objective measures are hampered by the use of hand-crafted stimuli which are hard to reproduce and manipulate. To tackle this, we developed a systematic method for generating 2D black-and-white pixel patterns using cellular automata and collected ratings of complexity and beauty from 80 participants. We developed various computational measures of pattern quantification such as density, entropies, local spatial complexity, Kolmogorov complexity, and asymmetries. We also introduced an "intricacy" measure quantifying the number of components in a pattern using a graph-based approach. We related these objective measures with participant judgments of complexity and beauty to find that a weighted combination of local spatial complexity and intricacy was an effective predictor (R-test (2)= .47) of complexity. This implies that people's complexity ratings depended on the local arrangement of pixels along with the global number of components in the pattern. Furthermore, we found a positive linear influence of complexity ratings on beauty, with a negative linear influence of disorder (asymmetry and entropy), and a negative interaction between the two quantities (R-test (2)= .65). This implies that there is beauty in complexity as long as there is sufficient order. Lastly, a moderated mediation analysis showed that subjective complexity mediates the influence of objective complexity (OC) on beauty, implying that subjective complexity provides useful information over and above OC.
