Cyclotomic Aperiodic Substitution Tilings
Stefan Pautze
Visualien der Breitbandkatze, Am Mitterweg 1, 85309 Pörnbach, Germany
Academic Editor: Hans Grimmer
Symmetry 2017, 9(2), 19; https://doi.org/10.3390/sym9020019
Received: 28 September 2016 / Revised: 18 December 2016 / Accepted: 4 January 2017 / Published: 25 January 2017
The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the -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 or , i.e., the tiling contains an infinite number of patches of any size with dihedral symmetry or only by iteration of substitution rules on a single tile.
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Keywords:
cyclotomic aperiodic substitution tiling; discrete metric geometry; quasiperiodic; nonperiodic; minimal inflation multiplier; minimal scaling factor; substitution matrix; Girih tiling
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Pautze, S. Cyclotomic Aperiodic Substitution Tilings. Symmetry 2017, 9, 19.
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