Patch frequencies in rhombic Penrose tilings.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2023-09-01 DOI:10.1107/S2053273323004990

Jan Mazáč

引用次数: 1

Abstract

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.

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菱形彭罗斯平铺中的贴片频率。

本文提出了一种有效的算法，用于精确计算菱形彭罗斯平铺的贴片频率。回顾了利用二值化构造彭罗斯平铺的方法，并通过扩展已知的获取顶点构型的方法，得到了所需的算法。然后用它来确定文献中出现的几个特别大的斑块的频率。类似的方法适用于一类特殊的瓷砖，这也详细解释了Ammann-Beenker瓷砖。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.