Connectedness of fractals associated with Arnoux-Rauzy substitutions

Details Connectedness of fractals associated with Arnoux-Rauzy substitutions Connectedness of fractals associated with Arnoux-Rauzy substitutions

2011-01-10

arxiv.org/abs/1101.1784v1

Mathematics

Combinatorics

15 pages, 7 figures

Scientific paper

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 planar sets, where each set is the projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the fractal associated with any finite product of Arnoux-Rauzy substitutions.

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