## Osaka Journal of Mathematics

### The computation of overlap coincidence in Taylor--Socolar substitution tiling

#### Abstract

Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of [1] to check overlap coincidence. It turns out that the tiling has overlap coincidence. So the tiling dynamics has pure point spectrum and we can conclude that this tiling has a quasicrystalline structure.

#### Article information

Source
Osaka J. Math., Volume 51, Number 3 (2014), 597-609.

Dates
First available in Project Euclid: 23 October 2014

https://projecteuclid.org/euclid.ojm/1414090793

Mathematical Reviews number (MathSciNet)
MR3272607

Zentralblatt MATH identifier
06368439

Subjects
Primary: 52C23: Quasicrystals, aperiodic tilings

#### Citation

Akiyama, Shigeki; Lee, Jeong-Yup. The computation of overlap coincidence in Taylor--Socolar substitution tiling. Osaka J. Math. 51 (2014), no. 3, 597--609. https://projecteuclid.org/euclid.ojm/1414090793

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