River networks exhibit a complex ramified structure that has inspired decadesof studies. Yet, an understanding of the propagation of a single stream remainselusive. Here we invoke a criterion for path selection from fracture mechanicsand apply it to the growth of streams in a diffusion field. We show that astream will follow local symmetry in order to maximize the water flux and thatits trajectory is defined by the local field in its vicinity. We also study thegrowth of a real network. We use this principle to construct the history of anetwork and to find a growth law associated with it. The results show that thedeterministic growth of a single channel based on its local environment can beused to characterize the structure of river networks.
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