A1 Refereed original research article in a scientific journal
Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry
Authors: Kari J, Rissanen M
Publisher: SPRINGER
Publication year: 2016
Journal: Discrete and Computational Geometry
Journal name in source: DISCRETE & COMPUTATIONAL GEOMETRY
Journal acronym: DISCRETE COMPUT GEOM
Volume: 55
Issue: 4
First page : 972
Last page: 996
Number of pages: 25
ISSN: 0179-5376
eISSN: 1432-0444
DOI: https://doi.org/10.1007/s00454-016-9779-1
Abstract
In this paper we prove the existence of quasiperiodic rhombic substitution tilings with 2n-fold rotational symmetry, for any n. The tilings are edge-to-edge and use rhombic prototiles with unit length sides. We explicitly describe the substitution rule for the edges of the rhombuses, and prove the existence of the corresponding tile substitutions by proving that the interior can be tiled consistently with the given edge substitutions.
In this paper we prove the existence of quasiperiodic rhombic substitution tilings with 2n-fold rotational symmetry, for any n. The tilings are edge-to-edge and use rhombic prototiles with unit length sides. We explicitly describe the substitution rule for the edges of the rhombuses, and prove the existence of the corresponding tile substitutions by proving that the interior can be tiled consistently with the given edge substitutions.
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