This chapter describes the experimental methodology used to investigate human perception of wallpaper group symmetry. We conducted three studies with a total of 147 participants, using a combination of forced-choice discrimination tasks, similarity judgments, and free-sorting paradigms.

Study 1 used a same/different paradigm to measure participants' ability to discriminate between patterns belonging to different wallpaper groups. Stimuli were generated algorithmically to control for low-level features (luminance, spatial frequency, element density) while varying only the symmetry group. This required developing a novel stimulus generation pipeline, described in detail in Section 3.2.

Study 2 employed a triad similarity judgment task. On each trial, participants saw three patterns and indicated which two were most similar. By sampling across all pairwise combinations of the 17 groups, we constructed a perceptual similarity space using multidimensional scaling.

Study 3 used a free-sorting paradigm in which participants organized printed pattern cards into groups of their choosing. This uncategorized approach reveals the natural categories that emerge from perception without imposing an experimenter-defined structure. The resulting clustering was analyzed using hierarchical methods and compared against the mathematical taxonomy.

All studies were conducted in accordance with Stanford IRB protocols, with participants recruited from the university community and compensated at standard rates.