ABSTRACT
This chapter aims to stochastic processes defined in terms of iterations of random functions. It illustrates the models in biology with ancestral type evolution processes, as well as in combinatorics and group theory with card shuffling techniques. The chapter is concerned with a series of iterated random processes arising in the construction and the analysis of fractal images. It is mainly taken from the seminal article of D. Aldous and P. Diaconis. A Cantor discontinuum subset of is a closed and nowhere dense and non-empty subset of the unit interval. Thus, the Lebesgue integral of this set is equal to zero. These "almost" empty fractal sets were introduced in 1883 by the German mathematician Georg Cantor.
