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arXiv:1506.06492cs.DM

An aperiodic set of 11 Wang tiles

Emmanuel Jeandel, Michael Rao

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Abstract

We present a new aperiodic tileset containing 11 Wang tiles on 4 colors, and we show that this tileset is minimal, in the sense that no Wang set with either fewer than 11 tiles or fewer than 4 colors is aperiodic. This gives a definitive answer to the problem raised by Wang in 1961.

arXiv comments
Journal reference
Advances in Combinatorics, 2021:1
DOI
doi:10.19086/aic.18614
Subjects
cs.DMDiscrete Mathematics cs.FLFormal Languages and Automata Theory

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  1. Pentagon Tiling Proof Solves Century-Old Math Problem 1 comment

    • Wang tiles, mentioned only at the end of the article, encode Turing-equivalent computation in their simple color-matching rule. It is unknown exactly how useful Wang tiles are to theory of computation, other than as a wonderful demonstration of how easily Turing-complete systems…

      DonbunEf7View on HNParent context

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