Tilings induced by a class of cubic Rauzy fractals
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Data
2013-03-18
Autores
Loridant, B.
Messaoudi, A. [UNESP]
Surer, P. [UNESP]
Thuswaldner, J. M.
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Resumo
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.
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Lattice tiling, Rauzy fractal, Self-replicating tiling, Substitution, Homeomorphic, Rauzy fractals, Topological properties, Substitution reactions, Topology, Fractals
Como citar
Theoretical Computer Science, v. 477, p. 6-31.