In the 1960’s, Hao Wang and Robert Berger produced a set of aperiodic tiles with matching rules that, if used to completely cover the plane, produce a pattern that is not similar to itself under translation. Smaller sets were discovered in the subsequent years, until the 1970’s when John Conway and Roger Penrose each found a set of two aperiodic tiles. The exhibit concerns Penrose’s tiling by thin and thick rhombuses.
a.periodicity, created by Duane Bailey and Debora Coombs, is comprised of aperiodic tilings constructed from a single tile that, when appropriately tilted in space, casts two shadows that correspond to Penrose’s rhombuses. These patches, all structurally identical, demonstrate different mathematical features of Penrose’s planar tilings. The sculptures are on display in the hallway outside of the Schow classrooms.