Self-organized percolation growth in regular and disordered lattices

The self-organized percolation process (SOP) is a growth model in which a critical percolation state is reached through self-organization. By controlling the number of sites or bonds in the growth front of the aggregate, the system is spontaneously driven to a stationary state that corresponds to approximately the percolation threshold of the lattice topology and percolation process. The SOP model is applied here to site and bond percolation in several regular lattices in two and three dimensions (triangular, honeycomb and simple cubic), as well as in a disordered network (Voronoi–Delaunai). Based on these results, we propose the use of this growth algorithm as a plausible model to describe the dynamics and the anomalous geometrical properties of some natural processes.