منابع مشابه
Self-Replicating Tiles and Their Boundary
All self-replicating lattice tilings of the plane can be constructed using special iterated function systems (IFS). Certain self-replicating curves can be constructed using the recurrent set method (RS). A bijection between the IFS parameters and the RS parameters is such that the curve K produced by the RS parameters is the boundary of the tile T produced by the IFS parameters. The corresponde...
متن کاملGenerating Self-Affine Tiles and Their Boundaries
A tile is a bounded subset of the plane, copies of which may be used to cover the whole plane without gaps or overlap. There are many sources (such as [1]) of beautiful images involving tiling, from medieval Islamic art, through Escher, to more modern work. Perhaps the simplest example of a tile, though, is a solid square, which may tile the plane in a familiar checkerboard pattern. The square ...
متن کاملRational Self-affine Tiles
An integral self-affine tile is the solution of a set equation AT = ⋃d∈D(T +d), where A is an n× n integer matrix and D is a finite subset of Z. In the recent decades, these objects and the induced tilings have been studied systematically. We extend this theory to matrices A ∈ Qn×n. We define rational self-affine tiles as compact subsets of the open subring R ×∏pKp of the adèle ring AK , where ...
متن کاملSelf-A ne Tiles
A self a ne tile in R is a set T of positive Lebesgue measure satisfying A T d D T d where A is an expanding n n real matrix with j det A j m an integer and D fd dmg R n a set of m digits Self a ne tiles arise in many contexts including radix expansions fractal geometry and the construction of compactly sup ported orthonormal wavelet bases of L R They are also studied as interesting tiles In th...
متن کاملSelf-Replicating and Self-Repairing Multicellular Automata
Biological organisms are among the most intricate structures known to man, exhibiting highly complex behavior through the massively parallel cooperation of numerous relatively simple elements, the cells. As the development of computing systems approaches levels of complexity such that their synthesis begins to push the limits of human intelligence, engineers are starting to seek inspiration in ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1999
ISSN: 0179-5376
DOI: 10.1007/pl00009433