Matching Rules and Substitution Tilings
Chaim Goodman-Strauss · Annals of Mathematics · 1998
A substitution tiling is a certain globally defined hierarchical structure in a geometric space; we show that for any substitution tiling in E n, n> 1, subject to relatively mild conditions, one can construct local rules that force the desired global structure to emerge. As an immediate corollary, infinite collections of forced aperiodic tilings are constructed.