V-Variable Fractals: Fractals with Partial Self Similarity

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a corresponding class of V-variable fractal sets or measures. These V-variable fractals can be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.Comment: 33 pages, 3 figure

Dimensions of random affine code tree fractals

We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.Comment: 22 page

PERFECT SAMPLING FROM THE LIMIT OF DETERMINISTIC PRODUCTS OF STOCHASTIC MATRICES

sampling from the limit of deterministi

Uniqueness of Invariant Measures for Place-Dependent Random Iterations of Functions

We give a survey of some results within the convergence theory for iterated random functions with an emphasis on the question of uniqueness of invariant probability measures for place-dependent random iterations with nitely many maps. Some problems for future research are pointed out