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Published in:
A Brief History of Aperiodic Crystals: 1962–2012 Read chapter Read first chapter

2013 | OriginalPaper | Chapter

8. The Ammann–Beenker Tilings Revisited

Authors : Nicolas Bédaride, Thomas Fernique

Published in: Aperiodic Crystals

Publisher: Springer Netherlands

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Abstract

This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclidean space. This family contains the Ammann–Beenker tilings as the solution of a simple optimization problem.

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previous chapter Octagon-Based Quasicrystalline Formations in Islamic Architecture
next chapter Substitution Rules and Topological Properties of the Robinson Tilings
Literature
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Katz A (1995) Matching rules and quasiperiodicity: the octagonal tilings. In: Axel F, Gratias D (eds) Beyond quasicrystals, pp 141–189 CrossRef
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Grünbaum B, Shephard GC (1986) Tilings and patterns. Freemann, New York
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Le TQT (1992) Necessary conditions for the existence of local rules for quasicrystals. Preprint
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Metadata
Title
The Ammann–Beenker Tilings Revisited
Authors
Nicolas Bédaride
Thomas Fernique
Copyright Year
2013
Publisher
Springer Netherlands
Book
Aperiodic Crystals

Print ISBN: 978-94-007-6430-9

Electronic ISBN: 978-94-007-6431-6

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-94-007-6431-6_8

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