Topological substitutions and Rauzy fractals
arXiv:1603.02790 · doi:10.24033/bsmf.2762
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.
29 pages, 13 figures.To appear. Bulletin de la Société Mathématiques de France. 2017