Tilings induced by a class of cubic Rauzy fractals

About the paper

coauthors Benoît Loridant
Ali Messaoudi
Jörg M. Thuswaldner
language English
published in Theoretical Computer Science 477 (2013)
pages 6 to 31
DOI 10.1016/j.tcs.2012.12.019
supported by FAPESP, process 2009/07744-0

Abstract

We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles asso- ciated 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.

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Theoretical Computer Science
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)