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. The reaction rate is calculated just as it would be calculated in the PDE approach, only here there is no diffusion since the cell has homogeneous concentration. Now diffusion is taken into account in the model by letting the species hop between cells in a probability proportional to the diffusion coefficient. 1 depicts one of the species participating in the reactions.
Dark cells are cells which have many of that species and brighter cells have little.
Black signifies more than 5 of that species for that cell. The report below shows the results gathered using this simulation program, it also details the algorithm. A masters thesis on the subject is also available. The model has the advantage that one can translate back and forth from the PDE formalism to the discrete-field formalism. This differs from some work already done with cellular automata that model reaction-diffusion.