Ozkaraca, Mustafa Ismail (2021) An application of space filling curves to substitution tilings. PhD thesis, University of Glasgow.
This is the latest version of this eprint.
|
PDF
Download (2MB) | Preview |
Abstract
We present an order structure for tiling substitution systems of the plane. The order structure gives rise to a space filling curve which is defined over an iterative system akin to the given tiling substitution. We use this space filling curve to define a label set on the original tiles, inducing a new tiling with a factor map to the original. On the other hand, our new tiling also defines an almost one-to-one factor map to a one-dimensional tiling obtained from ‘flattening’ the space filling curve. We view this as a way of reducing dimension, giving new insights on 2-dimensional substitution tilings using symbolic dynamics.
| Item Type: | Thesis (PhD) |
|---|---|
| Qualification Level: | Doctoral |
| Keywords: | Substitution tiling dynamical systems, space filling curves. |
| Subjects: | Q Science > QA Mathematics |
| Colleges/Schools: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Supervisor's Name: | Whittaker, Dr. Michael F. |
| Date of Award: | 2021 |
| Depositing User: | Mr Mustafa Ismail Ozkaraca |
| Unique ID: | glathesis:2021-81993 |
| Copyright: | Copyright of this thesis is held by the author. |
| Date Deposited: | 05 Feb 2021 17:10 |
| Last Modified: | 05 Feb 2021 17:23 |
| Thesis DOI: | 10.5525/gla.thesis.81993 |
| URI: | http://theses.gla.ac.uk/id/eprint/81993 |
Available Versions of this Item
- An application of space filling curves to substitution tilings. (deposited 05 Feb 2021 17:10) [Currently Displayed]
Actions (login required)
 |
View Item |
Download Statistics
Download Statistics