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Unimodular Pisot substitutions and their associated tiles

Jörg M. Thuswaldner (2006)

Journal de Théorie des Nombres de Bordeaux

Let σ be a unimodular Pisot substitution over a d letter alphabet and let X 1 , ... , X d be the associated Rauzy fractals. In the present paper we want to investigate the boundaries X i ( 1 i d ) of these fractals. To this matter we define a certain graph, the so-called contact graph 𝒞 of σ . If σ satisfies a combinatorial condition called the super coincidence condition the contact graph can be used to set up a self-affine graph directed system whose attractors are certain pieces of the boundaries X 1 , ... , X d . From this graph...

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