Look at any textbook on electromagnetism. Polarization is the response to an electric field. In isotropic materials, with linear response, it's proportional to the electric field, with the constant of proportionality the susceptibility. In anisotropic materials the constant's a tensor and in non-linear materials (e.g. ferroelectrics)  the response isn't linear in the field. Since the polarization, in any case, is  a vector, one can look, in particular, at its projection along the direction of the electric field and ask whether this projection is parallel or antiparallel to the electric field (so the sign is +1 or -1 respectively). And one can write a model, where only this sign is relevant, which one can then describe using cellular automata. The appropriate rule, that describes the time evolution, of course, does depend on how the direction of the polarization vector varies from site to site, from charge to charge-and here knowledge of electromagnetism is prerequisite.