Lots of aperiodic sets of tiles

摘要

Aperiodic tiling - a form of complex global geometric structure arising through locally checkable, constant-time matching rules - has long been closely tied to a wide range of physical, information-theoretic, and foundational applications, but its study and use has been hindered by a lack of easily generated examples. Through readily generalized, robust techniques for controlling hierarchical structure, we increase the catalogue of explicit constructions of aperiodic sets of tiles hundreds-fold, in lots, easily assembled and configured from atomic subsets of 211 tiles, enforcing 25,380 distinct "domino" substitution tiling systems. (C) 2018 Elsevier Inc. All rights reserved.