Abstract:The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the 2n-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmetry D n or D 2n , i.e., the tiling contains an infinite number of patches of any size with dihedral symmetry D n or D 2n only by iteration of substitution rules on a single tile.

We propose a definition for the similarity dimension of fractal curves with multiple generators.