Cellular automata models for the formation of Liesegang structures are proposed. This novel approach, which takes into account the fluctuations for the first time, describes the problem at a microscopic scale, in terms of reaction, diffusion, nucleation, and aggregation processes. We present large scale numerical simulations which provide clear verifications of the time and spacing laws and predict a novel behavior for the widths of the patterns. We show that two different microscopic reaction schemes are possible for producing Liesegang structures and we propose a phase diagram showing the different types of possible patterns.