Loridant, B.Messaoudi, A. [UNESP]Surer, P. [UNESP]Thuswaldner, J. M.2014-05-272014-05-272013-03-18Theoretical Computer Science, v. 477, p. 6-31.0304-3975http://hdl.handle.net/11449/74844We 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.6-31engLattice tilingRauzy fractalSelf-replicating tilingSubstitutionHomeomorphicRauzy fractalsTopological propertiesSubstitution reactionsTopologyFractalsArtigo10.1016/j.tcs.2012.12.019WOS:000316424700002Acesso restrito2-s2.0-848752201402111365241513122