Aperiodic tiles

Abstract

A set of tiles (closed topological disks) is called aperiodic if there exist tilings of the plane by tiles congruent to those in the set, but no such tiling has any translational symmetry. Several aperiodic sets have been discussed in the literature. We consider a number of aperiodic sets which were briefly described in the recent book Tilings and Patterns, but for which no proofs of their aperiodic character were given. These proofs are presented here in detail, using a technique with goes back to R. M. Robinson and Roger Penrose. © 1992 Springer-Verlag New York Inc.