Open dissipative systems, such as river networks, are known to exhibit self-organization with the tree network as the resulting signature pattern. Models that use the minimization constraint on energy expenditure have been successful in reproducing the branching tree patterns but the mechanism that enables the systems to find these extremal states remains elusive.We postulate that inherent random perturbation in the system environment is a sufficient condition for the generation of tree patterns. We demonstrate this, using a numerical river network evolution model driven by erosion-deposition processes under a gravitation gradient, and show that the minimization of energy expenditure is a consequent signature. Resulting river networks exhibit characteristics of natural river networks such as self-similarity, Hack's law, and power law in exceedance probability distribution of contributing area. Our finding in the evolutionary mechanism may serve as a motif for the formation of other networks.