Complex Geometries and Aperiodicity (End of Year 1 Report)

My 1st year Report for my research project 'Complex Geometries and Aperiodicity'. This document consists of a brief summary of this project while also supplying further details regarding the mathematics of this project.

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Ben Sinclair

Undergraduate Student, Durham University

My research project involves investigating how to create aperiodic, substitution tilings that contain different hierarchy levels so that a strange loop between these hierarchy levels is produced on various complex geometric grids. Much of the focus of this project is related to the complex geometry of the lithograph 'Print Gallery' by M.C. Escher.