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One-dimensional Substitution Tilings with an Interval Projection Structure

Edmund O. Harriss·Jeroen S. W. Lamb
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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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Edmund O. Harriss, Jeroen S. W. Lamb. 2006-01-09. One-dimensional Substitution Tilings with an Interval Projection Structure. https://arxiv.org/abs/math/0601187

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