|Topological substitutions and Rauzy fractals |
(Document sans référence bibliographique) 2016-03-09
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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.
Commentaires: 27 pages, 13 figures. arXiv admin note: text overlap with arXiv:1101.3905