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: Rauzy fractals, Arnoux-Rauzy substitutions, discrete planes
@article{ITA_2014__48_3_249_0,
author = {Berth\'e, Val\'erie and Jolivet, Timo and Siegel, Anne},
title = {Connectedness of fractals associated with {Arnoux-Rauzy} substitutions},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {249--266},
year = {2014},
publisher = {EDP Sciences},
volume = {48},
number = {3},
doi = {10.1051/ita/2014008},
mrnumber = {3302487},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ita/2014008/}
}
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 SP - 249 EP - 266 VL - 48 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ita/2014008/ DO - 10.1051/ita/2014008 LA - en ID - ITA_2014__48_3_249_0 ER -
%0 Journal Article %A Berthé, Valérie %A Jolivet, Timo %A Siegel, Anne %T Connectedness of fractals associated with Arnoux-Rauzy substitutions %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2014 %P 249-266 %V 48 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ita/2014008/ %R 10.1051/ita/2014008 %G en %F ITA_2014__48_3_249_0
Berthé, Valérie; Jolivet, Timo; Siegel, Anne. Connectedness of fractals associated with Arnoux-Rauzy substitutions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 249-266. doi: 10.1051/ita/2014008
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