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Article Dans Une Revue Bulletin de la société mathématique de France Année : 2018

Topological substitution for the aperiodic Rauzy fractal tiling

Résumé

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.

Dates et versions

hal-01322691 , version 1 (27-05-2016)

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Citer

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