Repetitive substitution tilings with respect to rigid motions
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 techniqu...
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| Main Authors: | , , |
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| Format: | text |
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Animo Repository
2018
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/5938 |
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| Institution: | De La Salle University |
| Summary: | 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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