Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 51, Number 3 (2014), 597-609.
The computation of overlap coincidence in Taylor--Socolar substitution tiling
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  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.
Osaka J. Math., Volume 51, Number 3 (2014), 597-609.
First available in Project Euclid: 23 October 2014
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 52C23: Quasicrystals, aperiodic tilings
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