Mampusti, M. and Whittaker, M. F. (2020) An aperiodic monotile that forces nonperiodicity through dendrites. Bulletin of the London Mathematical Society, 52(5), pp. 942-959. (doi: 10.1112/blms.12375)
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Abstract
We introduce a new type of aperiodic hexagonal monotile; a prototile that admits infinitely many tilings of the plane, but any such tiling lacks any translational symmetry. Adding a copy of our monotile to a patch of tiles must satisfy two rules that apply only to adjacent tiles. The first is inspired by the Socolar--Taylor monotile, but can be realised by shape alone. The second is a local growth rule; a direct isometry of our monotile can be added to any patch of tiles provided that a tree on the monotile connects continuously with a tree on one of its neighbouring tiles. This condition forces tilings to grow along dendrites, which ultimately results in nonperiodic tilings. Our local growth rule initiates a new method to produce tilings of the plane.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Mampusti, MIchael and Whittaker, Professor Mike |
| Authors: | Mampusti, M., and Whittaker, M. F. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Bulletin of the London Mathematical Society |
| Publisher: | Wiley |
| ISSN: | 0024-6093 |
| ISSN (Online): | 1469-2120 |
| Published Online: | 28 June 2020 |
| Copyright Holders: | Copyright © 2020 The Authors |
| First Published: | First published in Bulletin of the London Mathematical Society 52(5): 942-959 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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