On the Frequency Module of the Hull of a Primitive Substitution Tiling

Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitu...

全面介紹

Saved in:
書目詳細資料
Main Authors: Say-Awen, April Lynne D, Frettlöh, Dirk, De Las Peñas, Ma. Louise Antonette N
格式: text
出版: Archīum Ateneo 2022
主題:
在線閱讀:https://archium.ateneo.edu/mathematics-faculty-pubs/185
https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1190&context=mathematics-faculty-pubs
標簽: 添加標簽
沒有標簽, 成為第一個標記此記錄!
機構: Ateneo De Manila University
實物特徵
總結:Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitution. A method is presented on how to arrive at the frequency module of the hull of a primitive substitution tiling (the minimal -module, where is the set of integers) containing the absolute frequency of each of its patches. The method involves deriving the tiling's edge types and vertex stars; in the process, a new substitution is introduced on a reconstructed set of prototiles.