  The study of generalized iterated function systems (GIFS) was introduced by
Mihail and Miculescu in 2008. We provide a new approach to study those systems
as the limit of the Hutchinson-Barnsley setting for infinite iterated function
systems (IIFS) which has been developed by many authors in the last years. We
show that any attractor of a contractive generalized iterated function system
is the limit with respect to Hausdorff-Pompeiu metric of attractors of
contractive infinite iterated function systems. We also prove that any
Hutchinson measure for a contractive generalized iterated function system with
probabilities is the limit with respect to the Monge-Kantorovich metric of the
Hutchinson measures for contractive infinite iterated function systems with
probabilities.
