We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles associated to beta-substitutions related to the polynomial x 3 − ax 2 − bx − 1 for a ≥ b ≥ 1. In particular, we compute the corresponding boundary graphs, describing the adjacencies in the tilings. These graphs are a valuable tool for more advanced studies of the… (More)
In this paper, we prove that the circle multiplication associated with the shifted 'I% bonacci sequence: (2'2)) is associative for all s 2 5.
In this paper, we study arithmetical and topological properties of a class of tiling sets generated by numeration system. This allows us to compute Hausdorff dimensions of boundaries of these sets and to show that they are quasi-disks. Résumé. Dans ce papier nousétudions les propriétés arithmétiques et topologiques d'une classe d'ensembles auto-similaires… (More)
We study the boundary of the 3-dimensional Rauzy fractal E ⊂ R × C generated by the polynomial P (x) = x 4 − x 3 − x 2 − x − 1. The finite automaton characterizing the boundary of E is given explicitly. As a consequence we prove that the set E has 18 neighborhoods where 6 of them intersect the central tile E in a point. Our construction shows that the… (More)
In this paper, we study aperiodic and periodic tilings induced by the Rauzy Fractal and its subtiles associated to beta-substitutions related to the polynomial x 3 − ax 2 − bx − 1 for a ≥ b ≥ 1.