Repetitive substitution tilings with respect to rigid motions

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Archival Material/Manuscript

Publication Date

2018

Abstract

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

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Disciplines

Mathematics

Note

"A paper presented at the 21st Japan Conference on Discrete and Computational Geometry, Graphs, and Games (Ateneo de Manila University, Philippines, Sept. 1-3, 2018)"

Keywords

Tiling (Mathematics)

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