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Arithmetic discrete planes are quasicrystals

Valerie Berthe 1
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Arithmetic discrete planes can be considered as liftings in the space of quasicrystals and tilings of the plane generated by a cut and project construction. We first give an overview of methods and properties that can be deduced from this viewpoint. Substitution rules are known to be an efficient construction process for tilings. We then introduce a substitution rule acting on discrete planes, which maps faces of unit cubes to unions of faces, and we discuss some applications to discrete geometry.
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Conference papers
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00432377
Contributor : Valerie Berthe <>
Submitted on : Monday, November 16, 2009 - 12:30:22 PM
Last modification on : Thursday, May 24, 2018 - 3:59:21 PM

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  • HAL Id : lirmm-00432377, version 1

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Valerie Berthe. Arithmetic discrete planes are quasicrystals. DGCI'09: Discrete Geometry for Computer Imagery, Sep 2009, Montreal, Canada. pp.1-12. ⟨lirmm-00432377⟩

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