On Canonical Substitution Tilings

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Edmund O. Harriss: On Canonical Substitution Tilings. PhD Thesis. Imperial College London 2004.



This thesis is concerned with canonical substitution tilings. These are tilings generated by the canonical projection method which admit substitution rules, and include the famous Penrose tilings. We characterise all canonical substitution tilings and consider the question what the set of all substitution rules is for a given tiling. In many cases, including the Penrose tilings, we are able to characterise all the substitution rules for the tiling. Our methods are constructive and give an algorithm to construct the substitution rules and tilings.

Extended Abstract


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