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.
@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},
volume = {48},
year = {2014},
pages = {249-266},
doi = {10.1051/ita/2014008},
mrnumber = {3302487},
language = {en},
url = {http://dml.mathdoc.fr/item/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) pp. 249-266. doi : 10.1051/ita/2014008. http://gdmltest.u-ga.fr/item/ITA_2014__48_3_249_0/
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