2006/01/09 by Edmund Harriss, Harriss, Edmund O., Jeroen S. W. Lamb +1
Computer Science · Materials Science · #37B50 #37E05 #52C23 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Quasicrystal Structures and Properties #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0601187
openalex publication_date 2006/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).