Self-Affine Tilings with Several Tiles, I
نویسندگان
چکیده
منابع مشابه
Neighbours of Self–Affine Tiles in Lattice Tilings
Let T be a tile of a self-affine lattice tiling. We give an algorithm that allows to determine all neighbours of T in the tiling. This can be used to characterize the sets VL of points, where T meets L other tiles. Our algorithm generalizes an algorithm of the authors which was applicable only to a special class of self-affine lattice tilings. This new algorithm can also be applied to classes c...
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Let A be an expanding n n integer matrix with j det A j m A standard digit set D for A is any complete set of coset representatives for Z A Z Associated to a given D is a set T A D which is the attractor of an a ne iterated function system satisfying T d D T d It is known that T A D tiles R n by some subset of Z This paper proves that every standard digit set D gives a set T A D which tiles R w...
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Let A be an expanding n n integer matrix with j det(A)j = m. A standard digit set D for A is any complete set of coset representatives for Z n =A(Z n). Associated to a given D is a set T(A; D), which is the attractor of an aane iterated function system, satisfying T = d2D (T + d). It is known that T(A; D) tiles R n by some subset of Z n. This paper proves that every standard digit set D gives a...
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For a self similar or self a ne tile in R we study the following questions What is the boundary What is the convex hull We show that the boundary is a graph directed self a ne fractal and in the self similar case we give an algorithm to compute its dimension We give necessary and su cient conditions for the convex hull to be a polytope and we give a description of the Gauss map of the convex hull
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 ...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 1999
ISSN: 1063-5203
DOI: 10.1006/acha.1999.0268