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A substitution tiling is a certain globally de ned hierarchical structure in a geometric space; we show that for any substitution tiling in E d , d 1, subject to relatively mild conditions, one can construct local rules that force the desired global structure to emerge. As an immediate corollary, in nite collections of forced aperiodic tilings are constructed. The theorem covers all known examples of hierarchical aperiodic tilings. Figure 1: A substitution tiling On the left in gure 1, L-shapeddoi:10.2307/120988 fatcat:eu7by3no6zdt5kdjk3orvnfvza