We investigate the regular and moving Liesegang pattern formation phenomena in an open system. First, simulations have been performed at fixed coupling between the reactive medium and the reservoir, later this control parameter was varied during the simulations resulting in various phenomena. We predicted and monitored for the first time various--dynamically changing--precipitation structures and a spatial hysteresis phenomenon, which is beyond the scope of the Turing instability. The dynamics of the reaction is well detectable using specific quantities: the total amount of precipitate and its center of gravity.