منابع مشابه
Two-color Fractal Tilings
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...
متن کاملFractal 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...
متن کاملSome Hyperbolic Fractal Tilings
The concepts of fractal tiling and hyperbolic tiling are combined to create novel fractal surfaces in Euclidean threespace. Paper folding and computer modeling are used to create these constructs. We show examples using triangular, trapezoidal, and dart-shaped prototiles. Smaller tiles deflect out of the plane of adjacent larger tiles, resulting in nonplanar surfaces, the shapes of which are de...
متن کاملPSEUDO-SELF-AFFINE TILINGS IN Rd
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...
متن کاملFractal Tilings Based on Dissections of Polyhexes
Polyhexes, shapes made up of regular hexagons connected edge-to-edge, provide a rich source of prototiles for edge-to-edge fractal tilings. Numerous examples are given of fractal tilings with 2-fold and 3-fold rotational symmetry based on prototiles derived by dissecting polyhexes with 2-fold and 3-fold rotational symmetry, respectively. A systematic analysis is made of candidate prototiles bas...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1999
ISSN: 0263-6115
DOI: 10.1017/s1446788700036697