Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions

Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions

The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution. The simplest examples which correspond to algebraic parameters, ar...

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Bibliographic Details
Main Authors: Pierre Arnoux, Valerie Berthe, Hiromi Ei, Shunji Ito
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2001-01-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
substitutions
translations on compact groups
tilings
atomic surface
fractal sets
markov partitions
numeration systems
[info] computer science [cs]
[info.info-cg] computer science [cs]/computational geometry [cs.cg]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[math.math-co] mathematics [math]/combinatorics [math.co]
Online Access:https://dmtcs.episciences.org/2291/pdf

Internet

https://dmtcs.episciences.org/2291/pdf

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