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Connectedness of fractals associated with Arnoux-Rauzy substitutions (1101.1784v2)
Published 10 Jan 2011 in math.CO and cs.DM
Abstract: 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.