%0 Journal Article
%T Topological substitution for the aperiodic Rauzy fractal tiling
%+ Institut de Mathématiques de Marseille (I2M)
%+ Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon) (LIS)
%A Bedaride, Nicolas
%A Hilion, Arnaud
%A Jolivet, Timo
%Z 27 pages, 13 figures. arXiv admin note: text overlap with arXiv:1101.3905
%< avec comité de lecture
%@ 0037-9484
%J Bulletin de la société mathématique de France
%I Société Mathématique de France
%V 146
%N 3
%P 575-612
%8 2018
%D 2018
%Z 1603.02790
%R 10.24033/bsmf.2762
%K topological substitutions
%K Rauzy fractals
%K tilings
%K Tribonacci topological substitution
%K pointed topological substitution
%K Pisot substitutions
%Z Mathematics [math]/Dynamical Systems [math.DS]
%Z Mathematics [math]/Combinatorics [math.CO]Journal articles
%X 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.
%G English
%L hal-01322691
%U https://hal.science/hal-01322691
%~ UNIV-TLN
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TDS-MACS
%~ LIS-LAB
%~ ANR