Zoe Allwood

Exploring the Einstein Problem


The Einstein problem is an attempt to find an aperiodic prototile set that consists of a single tile. After some basic definitions and a more detailed explanation of the problem we look at the tile that fits this definition the best, created by Socolar and Taylor. The first chapter is an explanation of two of the ways this tile can be defined. The second chapter is a proof of the non-periodicity of all tilings created by this prototile based on the hierarchical structure of them. The third chapter is looking at the tile set as a substitution tiling creating an easier way to make tilings in a computer and also show all tilings are non-periodic more easily. The fourth shows other constructions of the tile, including a three dimensional one, and explorations into trying to improve the tile by trying to remove some of the issues with the tile in its current forms.

Zoe Allwood's thesis

Zoe Allwood's presentation

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