Utilizing randomness to generate complexity or realism in art and simulations of reality has been practiced for a number of decades in the movie, game, and digital art industries. In this project, we study how randomness can give rise to complex structures and the perception of beauty. By generating ensembles of random compositional pattern producing networks (CPPNs) and analyzing their image statistics in relation to perceptual scores of beauty, we investigate how randomness can be used to elicit the perception of complex structures and aesthetics.