Perceptual Similarities among Wallpaper Group Exemplars

Abstract

Symmetries are abundant within the visual environment, and many animals species are sensitive to visual symmetries. Wallpaper groups constitute a class of 17 regular textures that each contain a distinct combination of the four fundamental symmetries, translation, reflection, rotation and glide reflection, and together represent the complete set of possible symmetries in two-dimensional images. Wallpapers are visually compelling and elicit responses in visual brain areas that precisely capture the symmetry content of each group in humans and other primates. Here we ask to what extent different exemplars from the same wallpaper group are perceptually similar. We used an algorithm to produce a set of well-matched exemplars from 5 of the 17 wallpaper groups and instructed participants to freely sort the exemplars from each group into as many subsets as they wished based on any criteria they saw appropriate. P1, the simplest of the 17 groups, was consistently rated more self-similar than any other group, while the other four groups, although varying in symmetry content, were comparable in self-similarity. Our results suggest that except for the most extreme case (P1), perceived self-similarity of wallpaper groups is not directly tied to categories of symmetry based on group theory.