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Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry

Jarkko Kari, Markus Rissanen, Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry. Geometry 55(4), 972–996, 2016.

http://dx.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.

BibTeX entry:

@ARTICLE{uconv16983979,
  title = {Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry},
  author = {Kari, Jarkko and Rissanen, Markus},
  journal = {Geometry},
  volume = {55},
  number = {4},
  publisher = {Springer},
  pages = {972–996},
  year = {2016},
  keywords = {Substitution tiling;Quasiperiodic;Rotation symmetry;Rhombic tiling},
  ISSN = {0179-5376;1432-0444},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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