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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 tile set, the smallest known until now. Our construction is self-contained and organized to allow reasoning on properties of the resulting sets of tilings. With the help of this construction, we prove that this tileset has positive entropy. We also explain why this result was not expected.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01480693
Contributor : Bruno Durand <>
Submitted on : Wednesday, March 1, 2017 - 4:50:14 PM
Last modification on : Wednesday, May 19, 2021 - 12:38:01 PM
Long-term archiving on: : Tuesday, May 30, 2017 - 5:54:42 PM

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Bruno Durand, Guilhem Gamard, Anaël Grandjean. Aperiodic Tilings and Entropy. DLT: Developments in Language Theory, Aug 2014, Ekaterinburg, Russia. pp.166-177, ⟨10.1007/978-3-319-09698-8_15⟩. ⟨lirmm-01480693⟩

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