Tilings induced by a class of cubic Rauzy fractals - Loridant, B.; Messaoudi, A. [UNESP]; Surer, P. [UNESP]; Thuswaldner, J. M. (Elsevier, 2013)
We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles associated with beta-substitutions related to the polynomial x3-ax2-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 topological properties of the Rauzy fractals. As an example, we show that the Rauzy fractals are not homeomorphic to a closed disc as soon as a≤2b-4. The methods presented in this paper may be used to obtain similar results for other classes of substitutions.© 2012 Elsevier B.V. All rights reserved.
Keywords: Lattice tiling; Rauzy fractal; Self-replicating tiling; Substitution; Homeomorphic; Rauzy fractals; Topological properties; Substitution reactions; Topology; Fractals