Random affine code tree fractals and Falconer-Sloan condition
  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 $C(s)$. 
Esa J\"arvenp\"a\"a, Maarit J\"arvenp\"a\"a, Bing Li and \"Orjan   Stenflo
math.DS math.CA