Real Analysis Exchange

Dimension of Uniformly Random Self-Similar Fractals

Henna Koivusalo

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Abstract

The purpose of this note is to 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.

Article information

Source
Real Anal. Exchange, Volume 39, Number 1 (2013), 73-90.

Dates
First available in Project Euclid: 1 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1404230141

Mathematical Reviews number (MathSciNet)
MR3261900

Zentralblatt MATH identifier
1303.28013

Subjects
Primary: 28A80: Fractals [See also 37Fxx] 28A78: Hausdorff and packing measures
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Keywords
random fractal random self-similar set Hausdorff dimension

Citation

Koivusalo, Henna. Dimension of Uniformly Random Self-Similar Fractals. Real Anal. Exchange 39 (2013), no. 1, 73--90. https://projecteuclid.org/euclid.rae/1404230141


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