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.

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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

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