These autocatlytic processes are important in understanding many of the self-emergent phenomena. In the case of reaction diffusion processes the self-emergence is of spatial structures. The autocatlysis was shown to lead to the many of the interesting scaling laws which many phenomena exhibit. Recent articles by J.E. Pearson show that these kind of reactions can lead to dividing cell-like spots . Reactions are also modeled in the framework of lattice gas .
Localization can occur due to discretization.
A given reaction-diffusion process can be simulated by tracking the number and type of species in in the mixture. To this aim the reaction chamber is divided into small cells. Each of this cells is simulated in the mean-field approximation. This mean field approximation means that the concentration within each cell is assumed homogeneous. In a homogeneous solution the chance of a reaction taking place is proportional to the reaction rate.