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Aperiodic CrystalsFrom Modulated Phases to Quasicrystals:  Structure and Properties$
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Ted Janssen, Gervais Chapuis, and Marc de Boissieu

Print publication date: 2018

Print ISBN-13: 9780198824442

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198824442.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 06 March 2021

Tilings: mathematical models for quasicrystals

Tilings: mathematical models for quasicrystals

Chapter:
(p.111) 3 Tilings: mathematical models for quasicrystals
Source:
Aperiodic Crystals
Author(s):

Ted Janssen

Gervais Chapuis

Marc de Boissieu

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198824442.003.0003

This chapter discusses tilings as mathematical models for quasicrystals. In a first approximation quasicrystals may be described as being space filling with copies of two or more types of tiles. This description gives a connection with the mathematical notion of tilings, which have been well studied. A brief introduction of tilings is presented in this chapter along with the method of substitution to create aperiodic tilings. The symmetry of the tilings is also treated in this chapter, as are model sets and random tilings. Quasiperiodic crystals often have approximants, that is, periodic structures that are close to the aperiodic ones. The relations between quasiperiodic crystals and approximants also is described in this chapter.

Keywords:   tiling, aperiodic tiling, model set, approximant, random tiling

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