The necessary and su cient conditions for various self - similar sets and their dimension (
نویسنده
چکیده
We have given several necessary and su cient conditions for statistically self-similar sets and a.s. self-similar sets and have got the Hausdor dimension and exact Hausdor measure function of any a.s. self-similar set in this paper. It is useful in the study of probability properties and fractal properties and structure of statistically recursive sets. c © 2000 Elsevier Science B.V. All rights reserved. MSC: 60G10
منابع مشابه
Geometry of Self Affine Tiles I
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
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