Aperiodic tilings

摘要

Let X be a Riemannian manifold. An X-tiling system, or simply a tiling system where X is understood, is a finite collection J of colored compact subsets of X called tiles together with a finite set of rules controlling which finite (up to a bounded size) configurations of adjacent tiles are allowed ("admissible"). We shall consider only tiles C which are homeomorphic to balls in X. A tiling w is a partition (tessellation) of X o