We consider a model for the formation of a river network in which the erosion process plays a role only at the initial stage. Once a global connectivity is achieved, no further evolution takes place. In spite of this, the network reproduces approximately most of the empirical statistical results of the natural river network. It is observed that the resulting network is a spanning tree graph and therefore this process could be looked upon as a new algorithm for the generation of spanning tree graphs in which different configurations occur quasirandomly. A new loopless percolation model is also defined at an intermediate stage of evolution of the river network.

• Received 25 August 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.3460