Topological substitutions and Rauzy fractals

Abstract : We consider two families of planar self-similar tilings of different nature: the tilings consisting of translated copies of the fractal sets defined by an iterated function system, and the tilings obtained as a geometrical realization of a topological substitution (an object of purely combinatorial nature). We establish a link between the two families in a specific case, by defining an explicit topological substitution and by proving that it generates the same tilings as those associated with the Tribonacci Rauzy fractal.
Type de document :
Pré-publication, Document de travail
27 pages, 13 figures. arXiv admin note: text overlap with arXiv:1101.3905. 2016
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https://hal.archives-ouvertes.fr/hal-01322691
Contributeur : Aigle I2m <>
Soumis le : vendredi 27 mai 2016 - 14:57:01
Dernière modification le : lundi 4 mars 2019 - 14:04:19

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  • HAL Id : hal-01322691, version 1
  • ARXIV : 1603.02790

Citation

Nicolas Bedaride, Arnaud Hilion, Timo Jolivet. Topological substitutions and Rauzy fractals. 27 pages, 13 figures. arXiv admin note: text overlap with arXiv:1101.3905. 2016. 〈hal-01322691〉

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