Arithmetic Discrete Planes Are Quasicrystals

  • Valérie Berthé
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

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.

Keywords

digital planes arithmetic discrete planes tilings word combinatorics quasicrystals substitutions 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Valérie Berthé
    • 1
  1. 1.LIRMMUniversité Montpellier IIMontpellier Cedex 5France

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