Rapid convergence to frequency for substitution tilings of the plane. (English) Zbl 1232.05049

Summary: This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve.


05B45 Combinatorial aspects of tessellation and tiling problems
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
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