Arithmetic discrete planes are quasicrystals - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Conference Papers Year : 2009

Arithmetic discrete planes are quasicrystals

Valerie Berthe
  • Function : Author
  • PersonId : 938637


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.
No file

Dates and versions

lirmm-00432377 , version 1 (16-11-2009)


  • HAL Id : lirmm-00432377 , version 1


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


Gmail Facebook X LinkedIn More