Determining quasicrystal structures on substitution tilings

Quasicrystals are characterized by the diffraction patterns which consist of pure bright peaks. Substitution tilings are commonly used to obtain geometrical models for quasicrystals. We consider certain substitution tilings and show how to determine a quasicrystalline structure for the substitution tilings computationally. In order to do this, it is important to have the Meyer property on the substitution tilings. We use the recent result of Lee and Solomyak, which determines the Meyer property on the substitution tilings from the expansion maps.