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Topological substitution for the aperiodic Rauzy fractal tiling

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.
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https://hal.archives-ouvertes.fr/hal-01322691
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Submitted on : Friday, May 27, 2016 - 2:57:01 PM
Last modification on : Tuesday, March 3, 2020 - 1:23:06 AM

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Nicolas Bedaride, Arnaud Hilion, Timo Jolivet. Topological substitution for the aperiodic Rauzy fractal tiling. Bulletin de la société mathématique de France, Société Mathématique de France, 2018, 146 (3), pp.575-612. ⟨10.24033/bsmf.2762⟩. ⟨hal-01322691⟩

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