QGR geometer and mathematician Dugan Hammock presents a brief overview of two methods for generating quasicrystals: the multi-grid method and the cut-and-project method. Each construction method has a related algorithm for computing the Empires of a given collection of tiles. Plenty of computational results and graphics are shown of the 2D Penrose tiling and an analogous 3D quasicrystal called the Ammann tiling.
