Aperiodic tilings and entropy

Bruno Durand 1 Guilhem Gamard 1 Anaël Grandjean 1
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : In this paper, we present a construction of Kari–Culik aperiodic tileset. Our construction is self-contained and organized to allow reasoning on properties of the resulting sets of tilings. We prove that this tileset does not have any “unexpected behavior”, i.e., each line of each tiling has an average. Then we prove that this tileset has positive entropy, and that entropy is still positive when one adds some specific restrictions on the tilings. This shows that it is not self-similar, contrarily to all preceding aperiodic tilesets.
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Submitted on : Wednesday, March 1, 2017 - 3:59:07 PM
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Bruno Durand, Guilhem Gamard, Anaël Grandjean. Aperiodic tilings and entropy. Theoretical Computer Science, Elsevier, 2017, 666, pp.36-47. ⟨10.1016/j.tcs.2016.12.013⟩. ⟨lirmm-01480619⟩



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