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arnoux–rauzy substitutions

RAIRO - Theoretical Informatics and Applications (1)

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Connectedness of fractals associated with Arnoux–Rauzy substitutions
Valérie Berthé, Timo Jolivet, Anne Siegel
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 48 / Issue 3 / July 2014

Published online by Cambridge University Press:

27 May 2014, pp. 249-266

Print publication:

July 2014
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Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact sets, where each set is a renormalized projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the Rauzy fractal associated with any finite product of three-letter Arnoux–Rauzy substitutions.