NATO ASI Series Volume 354, 1999, pp 481-496

Aperiodic Hierarchical Tilings

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Abstract

A substitution tiling is a certain globally defined hierarchical structure in a geometric space. In [6] we show that for any substitution tiling in En, 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. Here we give an expository account of the construction. In particular, we discuss the use of hierarchical, algorithmic, geometrically sensitive coordinates—“addresses”, developed further in [9].