Remarks on Self-Affine Tilings
نویسندگان
چکیده
منابع مشابه
Remarks on Self-Affine Tilings
We study self-affine tilings of R n with special emphasis on the two-digit case. We prove that in this case the tile is connected and, if n 3, is a lattice-tile.
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An iterated function system Φ consisting of contractive affine mappings has a unique attractor F ⊆ R which is invariant under the action of the system, as was shown by Hutchinson [Hut]. This paper shows how the action of the function system naturally produces a tiling T of the convex hull of the attractor. These tiles form a collection of sets whose geometry is typically much simpler than that ...
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It is proved that every pseudo-self-affine tiling in R is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronöı tessellations is a corollary. Previously, these results were obtained in the planar case, jointly with Priebe Frank. The new approach is based on the theory of graph-directed iterated function systems and su...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 1994
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.1994.10504300