Article contents
Random affine code tree fractals and Falconer–Sloan condition
Published online by Cambridge University Press: 15 December 2014
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 Falconer and Sloan [Continuity of subadditive pressure for self-affine sets. Real Anal. Exchange 34 (2009), 413–427]. 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 $C(s)$.
- Type
- Research Article
- Information
- Copyright
- © Cambridge University Press, 2014
References
- 7
- Cited by