Numerical simulations of Liesegang systems are performed both with a prenucleation and a postnucleation model. Special interest is dedicated to two-dimensional morphological peculiarities of ring systems. With the prenucleation model, apparent bifurcations or branch points (anastomoses) can be created by adjacent trains of bands having different interband spaces or band positions shifted to each other. Spiral systems arise when the circular symmetry of concentric Liesegang rings is broken by at least one branch point. The postnucleation model comprises both formation of colloidal particles which form a turbidity zone and transition of these nuclei to solid particles which undergo Ostwald ripening at the expense of the colloids. The model demonstrates how Liesegang bands of solid particles arise from a primary turbidity zone which surrounds the expanding ring system. Because of rapid competitive particle growth, rings or bands may no longer grow continuously in transversal directions. They become arranged in chains of single filaments or spots forming a transversal rhythm. Finally, longitudinal alleys of gaps appear in continuous trains of Liesegang bands.