A new method to generate quasicrystalline structures : examples in 2D tilings

2014 We present a new algorithm for the generation of quasicrystalline structures. It is related to the cut and projection method, but allows a direct generation of the structure in the « physical » space E. The orthogonal space site selection is replaced by a direct check in a periodic array of « acceptance » regions in E. This method shows that there is a sort of underlying crystalline lattice in quasicrystals. We illustrate the construction in the 4D-2D cases with the 5-, 8-, 10and 12-fold symmetries which can be obtained by projection from 4D to 2D. Using this new method we also generate quasicrystals with a lower symmetry which have simple mean lattices. We present for instance a quasicrystal with a 4-fold symmetry. The points of this quasicrystal are a subset of the quasicrystal which has the whole 8-fold symmetry. J. Phys. France 51 (1990) 205-221 1er FÉVRIER 1990, Classification Physics Abstracts 61.40