Open Access
2013/2014 Dimension of Uniformly Random Self-Similar Fractals
Henna Koivusalo
Real Anal. Exchange 39(1): 73-90 (2013/2014).


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.


Download Citation

Henna Koivusalo. "Dimension of Uniformly Random Self-Similar Fractals." Real Anal. Exchange 39 (1) 73 - 90, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 1 July 2014

zbMATH: 1303.28013
MathSciNet: MR3261900

Primary: 28A78 , 28A80
Secondary: 60D05

Keywords: Hausdorff dimension , Random fractal , random self-similar set

Rights: Copyright © 2013 Michigan State University Press

Vol.39 • No. 1 • 2013/2014
Back to Top