Uploaded January 2018 | Updated September 2026, 3 weeks ago

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QGR geometer and mathematician Dugan presents a brief overview of two methods for generating quasicrystals: the multigrid 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.

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