2 research outputs found
Connectedness of fractals associated with Arnoux-Rauzy substitutions
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.Comment: 15 pages, v2 includes minor corrections to match the published
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Connectedness of fractals associated with Arnoux-Rauzy substitutions
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.