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2008 A substitution rule for the Penrose tiling
Kazushi Komatsu, Fumihiko Nakano
Nihonkai Math. J. 19(2): 111-135 (2008).

Abstract

We study the structure of the Penrose tiling (PT, in short) constructed by the matching rule, and deduce directly a substitution rule from that, which gives us (i)local configuration of the tiles,(ii) elementary proofs of the aperiodicity, the locally isomorphic property, and the uncountability,(iii) alternative proof of the fact that all PT's obtained by the matching rule can be constructed via the up-down generation.

Citation

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Kazushi Komatsu. Fumihiko Nakano. "A substitution rule for the Penrose tiling." Nihonkai Math. J. 19 (2) 111 - 135, 2008.

Information

Published: 2008
First available in Project Euclid: 18 March 2013

zbMATH: 1188.52022
MathSciNet: MR2490133

Subjects:
Primary: 52C23
Secondary: 05B45, 52C20

Rights: Copyright © 2008 Niigata University, Department of Mathematics

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Vol.19 • No. 2 • 2008
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