Complex Tilings

Bruno Durand; Leonid A. Levin; Alexander Shen

doi:10.2178/jsl/1208359062

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Complex Tilings

Bruno Durand·Leonid A. Levin·Alexander Shen

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Abstract

We study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling with O(n) Kolmogorov complexity of its n-by-n squares. We construct tile sets for which this bound is tight: all n-by-n squares in all tilings have complexity at least n. This adds a quantitative angle to classical results on non-recursivity of tilings -- that we also develop in terms of Turing degrees of unsolvability. Keywords: Tilings, Kolmogorov complexity, recursion theory

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Bruno Durand, Leonid A. Levin, Alexander Shen. 2001-07-04. Complex Tilings. https://doi.org/10.2178/jsl/1208359062

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