## Nihonkai Mathematical Journal

### A substitution rule for the Penrose tiling

#### 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.

#### Article information

Source
Nihonkai Math. J., Volume 19, Number 2 (2008), 111-135.

Dates
First available in Project Euclid: 18 March 2013

https://projecteuclid.org/euclid.nihmj/1363634624

Mathematical Reviews number (MathSciNet)
MR2490133

Zentralblatt MATH identifier
1188.52022

#### Citation

Komatsu, Kazushi; Nakano, Fumihiko. A substitution rule for the Penrose tiling. Nihonkai Math. J. 19 (2008), no. 2, 111--135. https://projecteuclid.org/euclid.nihmj/1363634624

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