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.
Citation
Shigeki Akiyama. Jeong-Yup Lee. "The computation of overlap coincidence in Taylor--Socolar substitution tiling." Osaka J. Math. 51 (3) 597 - 609, July 2014.