A DIFFUSION-LIMITED AGGREGATION MODEL FOR THE EVOLUTION OF DRAINAGE NETWORKS

We propose a modified diffusion-limited aggregation (DLA) model for th e evolution of fluvial drainage networks. Random walkers are introduce d randomly on a grid, and each two-dimensional random walk proceeds un til the walker finds a drainage network on which to accrete. This mode l for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages. The model also predicts stati stical features which agree with actual networks, including the freque ncy-order (bifurcation) ratio (R(b) - 3.98) and the stream length-orde r (R(r) = 2.09). Using the definition of network fractal dimension D = log R(b)/log R(r), we find that our DLA model gives D = 1.87, near th e observed range of D = 1.80-1.85.