Connectedness of fractals associated with Arnoux–Rauzy substitutions

Valérie Berthé; Timo Jolivet; Anne Siegel

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2014)

  • Volume: 48, Issue: 3, page 249-266
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Berthé, Valérie, Jolivet, Timo, and Siegel, Anne. "Connectedness of fractals associated with Arnoux–Rauzy substitutions." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 48.3 (2014): 249-266. <http://eudml.org/doc/273028>.

@article{Berthé2014,
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.},
author = {Berthé, Valérie, Jolivet, Timo, Siegel, Anne},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {Rauzy fractals; Arnoux–Rauzy substitutions; discrete planes; Rauzy fractal; three-letter substitutions; unimodular Pisot irreducible substitution; combinatorics on words},
language = {eng},
number = {3},
pages = {249-266},
publisher = {EDP-Sciences},
title = {Connectedness of fractals associated with Arnoux–Rauzy substitutions},
url = {http://eudml.org/doc/273028},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Berthé, Valérie
AU - Jolivet, Timo
AU - Siegel, Anne
TI - Connectedness of fractals associated with Arnoux–Rauzy substitutions
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 3
SP - 249
EP - 266
AB - 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.
LA - eng
KW - Rauzy fractals; Arnoux–Rauzy substitutions; discrete planes; Rauzy fractal; three-letter substitutions; unimodular Pisot irreducible substitution; combinatorics on words
UR - http://eudml.org/doc/273028
ER -

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