Fractal dual substitution tilings
نویسندگان
چکیده
منابع مشابه
Fractal Dual Substitution Tilings
Starting with a substitution tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles have fractal boundary. We show that each of the new tilings is mutually locally derivable to the original tiling. Thus, at the tiling space level, the new substitution rules are expressing...
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Two new series of substitution tilings are introduced in which the tiles appear in infinitely many orientations. It is shown that several properties of the well-known pinwheel tiling do also hold for these new examples, and, in fact, for all substitution tilings showing tiles in infinitely many orientations. Dedicated to my teacher Ludwig Danzer on the occasion of his 80th birthday
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The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the 2n-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmet...
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Introduction Substitution tilings have been discussed now for at least twenty-five years, initially motivated by the construction of hierarchical non-periodic structures in the Euclidean plane [?, ?, ?, ?]. Aperiodic sets of tiles were often created by forcing these structures to emerge. Recently, this line was more or less completed, with the demonstration that (essentially) every substitution...
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A variety of two-color fractal tilings (f-tilings) are described, in which no two adjacent tiles have the same color. Two-colorable examples from f-tilings that have been described previously are identified, and two techniques are used for converting f-tilings that are not two-colorable into new f-tilings that can be so colored. In the first of these, tiles are combined in order to change the v...
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ژورنال
عنوان ژورنال: Journal of Fractal Geometry
سال: 2016
ISSN: 2308-1309
DOI: 10.4171/jfg/37