This hands-on was for me the occasion to discover and to study a new kind of dynamical system which is a litlle bit different from the ones we have seen so far. Actually, I think that it was interesting to deal with these probabilistic cases to enlarge the notion of stability (in terms of probability) and to have some ideas about strange attractor, fractal sets and dimension.
What is totally amazing with this system is that at each time step the system evolves according to a random parameter, but that finally, there is an attractor which can be very well defined in terms of multi-fractal probability density functions.
Moreover, and that is the point that is used in image compression, with very few parameters, it is possible to encode very complex and beautiful images.