The box dimension of random box-like self-affine sets

Abstract

In this paper we study two random analogues of the box-like self-affine attractors introduced by Fraser, itself an extension of Sierpiński carpets. We determine the almost sure box-counting dimension for the homogeneous random case ($1$-variable random), and give a sufficient condition for the almost sure box dimension to be the expectation of the box dimensions of the deterministic attractors. Furthermore we find the almost sure box-counting dimension of the random recursive model ($\infty$-variable), which includes affine fractal percolation.

27 pages, 4 figures. Several small mistakes are addressed in this version

Cited by in corpus (2)

• Information fractal dimension of mass function
• The Assouad spectrum of random self-affine carpets