A diffusion-limited aggregation model for the evolution of drainage networks

Abstract

We propose a modified diffusion-limited aggregation (DLA) model for the evolution of fluvial drainage networks. Random walkers are introduced randomly on a grid, and each two-dimensional random walk proceeds until the walker finds a drainage network on which to accrete. This model for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages. The model also predicts statistical features which agree with actual networks, including the frequency-order (bifurcation) ratio ( R b = 3.98) and the stream length-order ( R r = 2.09). Using the definition of network fractal dimension D = logR blogR r, we find that our DLA model gives D = 1.87, near the observed range of D ≈ 1.80–1.85.