Witten-Sander DLA Model: Brownian Diffusion + Irreversible Aggregation Producing Self-Similar Fractals
Diffusion-Limited Aggregation (DLA) is a fractal growth model introduced by Witten and Sander in 1981. Particles undergo random walks (Brownian motion) and irreversibly stick upon contact with an existing aggregate, producing self-similar dendritic structures.
Algorithm: A seed particle is placed at the center. New walkers are launched from a circle surrounding the aggregate. Each walker performs a random walk until it touches the aggregate (stick) or wanders too far (respawn). The resulting structure exhibits fractal properties with a dimension typically around 1.71 in 2D.
Fractal Dimension: Estimated via the box-counting method. The aggregate is covered with grids of varying box sizes, and the scaling relationship N(s) ~ s^(-D) gives the fractal dimension D. A perfect DLA cluster in 2D has D ~ 1.71.
Applications: DLA models appear in electrochemical deposition, mineral dendrites, crystal growth, dielectric breakdown, vascular networks, river drainage patterns, urban growth, and lightning. The self-similar branching is a universal feature of diffusion-driven growth.
Use Play/Pause to control animation. Adjust emission rate and step size to change growth behavior. Try presets for different patterns.