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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Valérie Berthé, Timo Jolivet, Anne Siegel
• Keywords: CORR 2011, Education, Fractal, Fractal Boundary, Pisot Irreducible Substitution