Connectedness of Fractals Associated with Arnoux-Rauzy Substitutions - UTU Research Portal

A1 Refereed original research article in a scientific journal

Connectedness of Fractals Associated with Arnoux-Rauzy Substitutions

Authors: Valérie Berthé, Timo Jolivet, Anne Siegel

Publisher: EDP SCIENCES S A

Publishing place: LES ULIS CEDEX A; 17, AVE DU HOGGAR, PA COURTABOEUF, BP 112, F-91944 LES ULIS CEDEX A, FRANCE

Publication year: 2014

Journal: RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications

Journal name in source: Rairo-Theoretical Informatics and Applications

Journal acronym: Rairo-Theor.Inform.Appl.

Volume: 48

Issue: 3

First page : 249

Last page: 266

Number of pages: 18

ISSN: 0988-3754

DOI: https://doi.org/10.1051/ita/2014008

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.