One-dimensional substitution tilings with an interval projection structure

Abstract

We study nonperiodic tilings of the line obtained by a projection method with an interval projection structure. We obtain a geometric characterisation of all interval projection tilings that admit substitution rules and describe the set of substitution rules for each such a tiling. We show that each substitution tiling admits a countably infinite number of nonequivalent substitution rules. We also provide a complete description of all tilings of the line and half line with an interval projection structure that are fixed by a substitution rule. Finally, we discuss how our results relate to renormalization properties of interval exchange transformations (with two or three intervals).

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Cite this paper

@inproceedings{Harriss2008OnedimensionalST, title={One-dimensional substitution tilings with an interval projection structure}, author={E. O. Harriss and J. S. W. Lamb}, year={2008} }