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

Shigeki Akiyama, Jeong-Yup Lee
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 \cite{AL} 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.
View original: http://arxiv.org/abs/1212.4209