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arXiv · 1512.07022

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

Sascha Troscheit
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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.

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Sascha Troscheit. 2017-05-19. The box dimension of random box-like self-affine sets. https://doi.org/10.1512/iumj.2018.67.7295

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