An application of space filling curves to substitution tilings

Ozkaraca, Mustafa Ismail (2021) An application of space filling curves to substitution tilings. PhD thesis, University of Glasgow.

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: https://theses.gla.ac.uk/id/eprint/81993