Journal of Integer Sequences, Vol. 16 (2013), Article 13.2.14

Examples of Substitution Systems and Their Factors

Michael Baake and Franz Gähler
Fakultät für Mathematik
Universität Bielefeld
Postfach 100131
33501 Bielefeld

Uwe Grimm
Department of Mathematics and Statistics
The Open University
Walton Hall
Milton Keynes MK7 6AA
United Kingdom


The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical system, one can reach a better understanding of spectral and topological properties. We illustrate this point of view by means of some characteristic examples, including a rather universal substitution in one dimension as well as the squiral and the table tilings of the plane.

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Received August 15 2012; revised version received December 10 2012. Published in Journal of Integer Sequences, March 2 2013.

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