  The Abelian sandpile model was the first example of a self-organized critical
system studied by Bak, Tang and Wiesenfeld. The dynamics of the sandpiles occur
when the grains topple over a graph. In this study, we allow the graph to
evolve over time and change the topology at each stage. This turns out in the
occurrence of phenomena impossible in the classical sandpile models. For
instance, configurations over evolutive graphs that are always unstable. We
also experiment with the stabilization of configurations with a large number of
grains at the center over evolutive graphs, this allows us to obtain
interesting fractals. Finally, we obtain some power laws associated with some
evolutive graphs.
