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A stochastic lattice gas automata model for formation of river networks is proposed. The model is based on two-dimensional lattice gas automata with three fundamental principles at each node. The water source is regarded as a fixed point where a drop of water drips every time step. This system can be treated as a memory network: the probability of water moving along a direction relies on the history of the channel segment along which water drops have moved. Last, we find that the width of the river channel and the number of channels with this width meet a scaling law when the system reaches a critical status.

Simple stochastic lattice gas automaton model for formation of river networks