Generalized Percolation Processes Using Pretopology Theory

We propose in this paper a generalization of percolation processes in Z
²
using the pretopology theory. We formalize the notion of neighborhood by extending it to the concept of proximity, expressing different types of connections that may exist between the elements of a population. A modeling and simulation of forest fire using this approach shows the efficiency of this formalism to provide a realistic and powerful modeling of complex systems.