Substitution tilings with dense tile orientations and n-fold rotational symmetry

• Main Authors: Frettlöh, Dirk, Say-Awen, April Lynne D, De Las Peñas, Ma. Louise Antonette N
• Format: text
• Published: Archīum Ateneo 2017
• Subjects: Tilings; Aperiodic order; Irrational angle; Geometry and Topology; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/11; https://www.sciencedirect.com/science/article/pii/S0019357716300763
• Institution: Ateneo De Manila University

It is shown that there are primitive substitution tilings with dense tile orientations invariant under n-fold rotation for n∈{2,3,4,5,6,8}. The proof for dense tile orientations uses a general result about irrationality of angles in certain parallelograms.