Patch frequencies in rhombic Penrose tilings

Mazáč J (2023)
Acta Crystallographica Section A Foundations and Advances 79(5): 13.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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DOI
URN
urn:nbn:de:0070-pub-29812837
Autor*in
Mazáč, JanUniBi
Einrichtung
Fakultät für Mathematik
Abstract / Bemerkung
This exposition presents an efficient algorithm for an exact calculation of patch frequencies for rhombic Penrose tilings. A construction of Penrose tilings via dualization is recalled and, by extending the known method for obtaining vertex configurations, the desired algorithm is obtained. It is then used to determine the frequencies of several particularly large patches which appear in the literature. An analogous approach works for a particular class of tilings and this is also explained in detail for the Ammann–Beenker tiling.
Erscheinungsjahr
2023
Zeitschriftentitel
Acta Crystallographica Section A Foundations and Advances
Band
79
Ausgabe
5
Seite(n)
13
Urheberrecht / Lizenzen
Creative Commons Namensnennung 4.0 International Public License (CC-BY 4.0)
eISSN
2053-2733
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
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https://pub.uni-bielefeld.de/record/2981283

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Mazáč J. Patch frequencies in rhombic Penrose tilings. Acta Crystallographica Section A Foundations and Advances. 2023;79(5):13.
Mazáč, J. (2023). Patch frequencies in rhombic Penrose tilings. Acta Crystallographica Section A Foundations and Advances, 79(5), 13. https://doi.org/10.1107/S2053273323004990
Mazáč, Jan. 2023. “Patch frequencies in rhombic Penrose tilings”. Acta Crystallographica Section A Foundations and Advances 79 (5): 13.
Mazáč, J. (2023). Patch frequencies in rhombic Penrose tilings. Acta Crystallographica Section A Foundations and Advances 79, 13.
Mazáč, J., 2023. Patch frequencies in rhombic Penrose tilings. Acta Crystallographica Section A Foundations and Advances, 79(5), p 13.
J. Mazáč, “Patch frequencies in rhombic Penrose tilings”, Acta Crystallographica Section A Foundations and Advances, vol. 79, 2023, pp. 13.
Mazáč, J.: Patch frequencies in rhombic Penrose tilings. Acta Crystallographica Section A Foundations and Advances. 79, 13 (2023).
Mazáč, Jan. “Patch frequencies in rhombic Penrose tilings”. Acta Crystallographica Section A Foundations and Advances 79.5 (2023): 13.
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2023-07-28T10:05:20Z
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