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arXiv · 0810.5225

Substitution Tilings and Separated Nets with Similarities to the Integer Lattice

Yaar Solomon
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Abstract

We show that any primitive substitution tiling of the plane creates a separated net which is biLipschitz to the integer lattice. Then we show that if H is a primitive Pisot substitution in an Euclidean space, for every separated net Y, that corresponds to some tiling of the tiling space, there exists a bijection F between Y and the integer lattice that translate every element of Y a bounded distance. As a corollary we get that we have such an F for any separated net that corresponds to a Penrose Tiling. The proofs rely on results of Laczkovich, and Burago and Kleiner.

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Yaar Solomon. 2009-01-18. Substitution Tilings and Separated Nets with Similarities to the Integer Lattice. https://arxiv.org/abs/0810.5225

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