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arXiv · 1404.2473

Random affine code tree fractals and Falconer-Sloan condition

Esa Järvenpää·Maarit Järvenpää·Bing Li·Örjan Stenflo
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Abstract

We calculate the almost sure dimension for a general class of random affine code tree fractals in $\mathbb R^d$. The result is based on a probabilistic version of the Falconer-Sloan condition $C(s)$ introduced in \cite{FS}. We verify that, in general, systems having a small number of maps do not satisfy condition $C(s)$. However, there exists a natural number $n$ such that for typical systems the family of all iterates up to level $n$ satisfies condition $C(s)$.

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Esa Järvenpää, Maarit Järvenpää, Bing Li, Örjan Stenflo. 2014-09-16. Random affine code tree fractals and Falconer-Sloan condition. https://arxiv.org/abs/1404.2473

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