Comparison of models and lattice-gas simulations for Liesegang patterns

For more than a century Liesegang patterns -- self-organized, quasi-periodic structures occurring in diffusion-limited chemical reactions with two components -- have been attracting scientists. The pattern formation can be described by four basic empirical laws. In addition to many experiments, several models have been devised to understand the formation of the bands and rings. Here we review the most important models and complement them with detailed three-dimensional lattice-gas simulations. We show how the mean-field predictions can be reconciled with experimental data by a redefinition of the distances suggested by our lattice-gas simulations.