Dimension of uniformly random self-similar fractals
Dynamical Systems
2015-05-11 v2 Probability
Abstract
We calculate the almost sure Hausdorff dimension of uniformly random self-similar fractals. These random fractals are generated from a finite family of similarities, where the linear parts of the mappings are independent uniformly distributed random variables at each step of iteration. We also prove that the Lebesgue measure of such sets is almost surely positive in some cases.
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Cite
@article{arxiv.1305.1603,
title = {Dimension of uniformly random self-similar fractals},
author = {Henna Koivusalo},
journal= {arXiv preprint arXiv:1305.1603},
year = {2015}
}
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13 pages