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Paul Erdős: Life and Work Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Remarks on Penrose Tilings

Author : N. G. de Bruijn

Published in: The Mathematics of Paul Erdős I

Publisher: Springer New York

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Abstract

This paper will cover some details on Penrose tilings presented in lectures over the years but never published in print before. The main topics are: (i) the characterizability of Penrose tilings by means of a local rule that does not refer to arrows on the edges of the tiles, and (ii) the fact that the Ammann quasigrid of the inflation of a Penrose tiling is topologically equivalent to the pentagrid that generates the original tiling.

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previous chapter Extension of Functional Equations
next chapter Distances in Convex Polygons
Literature
1.
N. G. de Bruijn, Algebraic theory of Penrose’s non-periodic tilings of the plane. Kon. Nederl. Akad. Wetensch. Proc. Ser. A 84 ( = Indagationes Mathematicae 43), 38–52 and 53–66 (1981). Reprinted in: P. J. Steinhardt and Stellan Ostlund: The Physics of Quasicrystals, World Scientific Publ., Singapore, New Jersey, Hong Kong.
2.
N.G. de Bruijn, Dualization of multigrids. In: Proceedings of the International Workshop Aperiodic Crystals, Les Houches 1986. Journal de Physique, Vol. 47, Colloque C3, supplement to nr. 7, July 1986, pp. 9–18.
3.
N. G. de Bruijn, A riffle shuffle card trick and its relation to quasicrystal theory. Nieuw Archief Wiskunde (4) 5 (1987) 285–301.
4.
N. G. de Bruijn, Symmetry and quasisymmetry. In: Symmetrie in Geistes- und Naturwissenschaft. Herausg. R. Wille. Springer Verlag 1988, pp. 215–233.
5.
N. G. de Bruijn, Updown generation of Penrose tilings, Indagationes Mathematicae, N.S., 1, pp. 201–219 (1990).
6.
Martin Gardner, Mathematical games. Extraordinary nonperiodic tiling that enriches the theory of tiles. Scientific American 236 (1) 110–121 (Jan. 1977).
7.
Branko Grünbaum and G. C. Shephard. Tilings and patterns. New York, W.H. Freeman and Co. 1986.
8.
9.
J. E. S. Socolar and P. J. Steinhardt. Quasicrystals. II. Unit cell configurations. Physical Rev. B Vol. 34 (1986), 617–647. Reprinted in: P.J. Steinhardt and Stellan Ostlund: The Physics of Quasicrystals, World Scientific Publ., Singapore, New Jersey, Hong Kong.
Metadata
Title
Remarks on Penrose Tilings
Author
N. G. de Bruijn
Copyright Year
2013
Publisher
Springer New York
Book
The Mathematics of Paul Erdős I

Print ISBN: 978-1-4614-7257-5

Electronic ISBN: 978-1-4614-7258-2

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-7258-2_29

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