Connectedness of fractals associated with Arnoux-Rauzy substitutions
Combinatorics
2019-02-20 v2 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1101.1784,
title = {Connectedness of fractals associated with Arnoux-Rauzy substitutions},
author = {Valérie Berthé and Timo Jolivet and Anne Siegel},
journal= {arXiv preprint arXiv:1101.1784},
year = {2019}
}
Comments
15 pages, v2 includes minor corrections to match the published version