## Matrices of 3-iet preserving morphisms

- Petr Ambroz, Zuzana Masáková, Edita Pelantová
- Theor. Comput. Sci.
- 2008

1 Excerpt

- Published 2008

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).

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