Equivalences (i-MLD) of Tilings and Tiling Spaces
نویسندگان
چکیده
منابع مشابه
Tilings, Tiling Spaces and Topology
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical properties of the space (such as mixing, or the spectrum of the translation operator) are closely related to bulk properties of individual tilings (such as th...
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15 صفحه اولTriangle Tiling III: The Triquadratic Tilings
An N-tiling of triangle ABC by triangle T (the “tile”) is a way of writing ABC as a union of N copies of T overlapping only at their boundaries. We continue the work of [1, 2] on classifying the possible triangle tilings. The results of all three papers together enable us to make some progress on two problems of Erdős about triangle tilings, one of which asks, “for which N is there an N-tiling ...
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We investigate the dynamics of tiling dynamical systems and their deformations. If two tiling systems have identical combinatorics, then the tiling spaces are homeomorphic, but their dynamical properties may differ. There is a natural map I from the parameter space of possible shapes of tiles to H of a model tiling space, with values in R. Two tiling spaces that have the same image under I are ...
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ژورنال
عنوان ژورنال: Journal of Applied & Computational Mathematics
سال: 2019
ISSN: 2168-9679
DOI: 10.4172/2168-9679.1000434