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Conference Papers Year : 2007

Topological properties of central tiles for substitutions


Central tiles are compact set with fractal boundary that are generated by beta-numeration or substitution numeration systems. They usually generate a self-replicating substitution tiling. Pictures show that there is a large variety of topological properties for these tiles. In this talk, we make use of information on intersections in the self-replicating substitution tiling to deduce sufficient conditions for topological properties, such as connectivity, 0 inner point, homeomorphism to a closed disk and not free fundamental group. These conditions can be checked algorithmically for each given example.
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inria-00180246 , version 1 (18-10-2007)


  • HAL Id : inria-00180246 , version 1


Anne Siegel, Jorg Thuswaldner. Topological properties of central tiles for substitutions. Journées de Numération, Apr 2007, Graz, Austria. ⟨inria-00180246⟩
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