The compact sets invariant with respect to an Iterated (finite) Function System (IFS) have been studied very intensively during last decades by Mandelbrot, Dekking, Hutchinson, Barnsley and many others.

In this paper, it is considered the case of the countable system of contraction maps on a compact metric space X and the contraction map associated to it is defined on the complete metric space of all non-empty compact subset of X endowed with the Hausdorff metric.

We show that the attractor associated to the sequence of contraction maps is approximated by the attractors of the partial systems