Issue |
RAIRO-Theor. Inf. Appl.
Volume 48, Number 3, July-August 2014
Special issue in the honor of the 14th “Journées montoises d’informatique théorique”. I.
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Page(s) | 249 - 266 | |
DOI | https://doi.org/10.1051/ita/2014008 | |
Published online | 27 May 2014 |
Connectedness of fractals associated with Arnoux–Rauzy substitutions
1 LIAFA, CNRS, Université Paris
Diderot, Case 7014, 75205
Paris Cedex 13,
France.
berthe@liafa.univ-paris-diderot.fr
2 Department of Mathematics, University
of Turku 20014, Finland.
3 INRIA, Centre Rennes-Bretagne
Atlantique, Dyliss, Rennes, France.
Received:
14
March
2014
Accepted:
14
March
2014
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.
Mathematics Subject Classification: 68R15 / 37B10
Key words: Rauzy fractals / Arnoux–Rauzy substitutions / discrete planes
© EDP Sciences 2014
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