Repetitive substitution tilings with respect to rigid motions

• Main Authors: Say-Awen, April Lynne D., De las Peñas, Ma. Louise Antonette N., Frettlöh, Dirk
• Format: text
• Published: Animo Repository 2018
• Subjects: Tiling (Mathematics); Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/5938
• Institution: De La Salle University

A tiling T is repetitive for every r > 0 there exists R = R (r) > 0 such that every R-patch of T contains an equivalent copy of every r-patch of T. in this paper, we describe a construction of a substitution that gives rise to a repetitive tiling T* with respect to rigid motions. The technique applied in the construction­ involves defining dissection rules on inflated edges of tiles and assigning orientations on edges tiles. Other properties pertaining to T* will be presented. One property is the occurrence of dense tile orientation T*. By dense tile orientations (DTO), we mean the orientations of tiles in the tiling are dense in a unit circle. To date, examples of this class of tilings are rarely found in the literature