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RANDOM SUBSETS OF SELF-AFFINE FRACTALS

Part of: Geometric probability and stochastic geometry Classical measure theory

Published online by Cambridge University Press:  10 December 2009

Kenneth Falconer  and
Jun Miao
Kenneth Falconer
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, U.K. (email: kjf@st-andrews.ac.uk)
Jun Miao
Affiliation:
Department of Mathematics, East China Normal University, 3663 Zhong Shan North Road, Shanghai 200062, China (email: jjmiao@math.ecnu.edu.cn)

Abstract

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We find the almost-sure Hausdorff and box-counting dimensions of random subsets of self-affine fractals obtained by selecting subsets at each stage of the hierarchical construction in a statistically self-similar manner.

MSC classification

Secondary: 28A80: Fractals 60D05: Geometric probability and stochastic geometry

Information

Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010 , pp. 61 - 76
Copyright
Copyright © University College London 2010

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