Numerical simulations show that a simple model for the formation of Liesegang precipitation patterns, which takes into account the dependence of nucleation and particle growth kinetics on supersaturation, can explain not only simple patterns like parallel bands in a test tube or concentric rings in a petri dish, but also more complex structural features, such as dislocations, helices, "Saturn rings," or patterns formed in the case of equal initial concentrations of the source substances. The limits of application of the model are discussed. (c) 1994 American Institute of Physics.