Cyclotomic Aperiodic Substitution Tilings
Visualien der Breitbandkatze, Am Mitterweg 1, 85309 Pörnbach, Germany
Academic Editor: Hans Grimmer
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
, i.e., the tiling contains an infinite number of patches of any size with dihedral symmetry
only by iteration of substitution rules on a single tile.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Pautze, S. Cyclotomic Aperiodic Substitution Tilings. Symmetry 2017, 9, 19.
Pautze S. Cyclotomic Aperiodic Substitution Tilings. Symmetry. 2017; 9(2):19.
Pautze, Stefan. 2017. "Cyclotomic Aperiodic Substitution Tilings." Symmetry 9, no. 2: 19.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.