Diffusion Limited Aggregation (DLA) is a model for non-equilibrium growth, where growth is determined by diffusing particles. It can model e.g. a Bacillus subtilis bacteria colony in a petri dish. The idea is that the colony feeds on nutrients in the immediate environment, that the probability of growth is determined by the concentration of nutrients and finally that the concentration of nutrients in its turn is determined by diffusion.
You can read my report at docs folder to understand more.