A Family of Non-Periodic Tilings of the Plane by Right Golden Triangles

被引：1
|
作者：
Vereshchagin, Nikolay [1 ]
机构：
[1] HSE Univ, Moscow, Russia
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2022年 / 68卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
Substitution tiling; Golden right triangle; Sofic tiling; Local rule; Non-periodic tiling; RULES;
D O I：
10.1007/s00454-021-00367-4
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We study a family of substitution tilings with similar right triangles of two sizes which is obtained using the substitution rule introduced in Danzer and van Ophuysen (Res. Bull. Panjab Univ. Sci. 50(1-4), 137-175 (2000)). In that paper, it is proved this family of tilings can be obtained from a local rule using decorated tiles. That is, that this family is sofic. In the present paper, we provide an alternative proof of this fact. We use more decorated tiles than Danzer and van Ophuysen (22 in place of 10). However, our decoration of supertiles is more intuitive and our local rule is simpler.
引用
收藏
页码：188 / 217
页数：30
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