Self-Similar Transformation and Vertex Configurations of the Octagonal Ammann–Beenker Tiling
Hong-Mei Zhang, Cheng Cai, Xiu-Jun Fu**
School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640
Abstract ：Based on the matching rules for squares and rhombuses, we study the self-similar transformation and the vertex configurations of the Ammann–Beenker tiling. The structural properties of the configurations and their relations during the self-similar transformation are obtained. Our results reveal the distribution correlations of the configurations, which provide an intuitive understanding of the octagonal quasi-periodic structure and also give implications for growing perfect quasi-periodic tiling according to the local rules.
收稿日期: 2017-12-27
出版日期: 2018-05-19
:
61.44.Br
(Quasicrystals)
61.50.Ah
(Theory of crystal structure, crystal symmetry; calculations and modeling)
02.60.Cb
(Numerical simulation; solution of equations)
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2018, Vol. 35 
