License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.AUTOMATA.2021.9
URN: urn:nbn:de:0030-drops-140182
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14018/
Go to the corresponding OASIcs Volume Portal

Lutfalla, Victor H.

An Effective Construction for Cut-And-Project Rhombus Tilings with Global n-Fold Rotational Symmetry

pdf-format:
OASIcs-AUTOMATA-2021-9.pdf (0.8 MB)

Abstract

We give an explicit and effective construction for rhombus cut-and-project tilings with global n-fold rotational symmetry for any n. This construction is based on the dualization of regular n-fold multigrids. The main point is to prove the regularity of these multigrids, for this we use a result on trigonometric diophantine equations. A SageMath program that computes these tilings and outputs svg files is publicly available in [Lutfalla, 2021].

BibTeX - Entry

@InProceedings{lutfalla:OASIcs.AUTOMATA.2021.9,
  author =	{Lutfalla, Victor H.},
  title =	{{An Effective Construction for Cut-And-Project Rhombus Tilings with Global n-Fold Rotational Symmetry}},
  booktitle =	{27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)},
  pages =	{9:1--9:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-189-4},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{90},
  editor =	{Castillo-Ramirez, Alonso and Guillon, Pierre and Perrot, K\'{e}vin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14018},
  URN =		{urn:nbn:de:0030-drops-140182},
  doi =		{10.4230/OASIcs.AUTOMATA.2021.9},
  annote =	{Keywords: Cut-and-project tiling, Rhombus tiling, Aperiodic order, Rotational symmetry, De Bruijn multigrid, Trigonometric diophantine equations}
}

Keywords: Cut-and-project tiling, Rhombus tiling, Aperiodic order, Rotational symmetry, De Bruijn multigrid, Trigonometric diophantine equations
Collection: 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021)
Issue Date: 2021
Date of publication: 28.06.2021
Supplementary Material: n-fold multigrid dual tilings [Lutfalla, 2021]
Software: https://doi.org/10.5281/zenodo.4698387

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI