Origins
DLA was introduced by T. A. Witten and L. M. Sander in 1981 to model electrodeposition, dielectric breakdown, and other pattern-forming processes driven by diffusion.
Algorithm
- Place a seed particle at the centre of the grid.
- Spawn a walker at a random position near the boundary.
- The walker performs a 2-D random walk (Brownian motion).
- If it steps adjacent to any settled particle, it sticks permanently and becomes part of the cluster.
- Repeat with new walkers until the structure reaches the desired size.
The aggregate's growth is diffusion-limited because particles far from the frontier have little chance of sticking. The pattern exhibits a fractal dimension ≈ 1.71 in 2-D.
Visualiser Details
- We track live walkers in an array, recycling them once they stick.
- 2000 simulation steps are executed per animation frame for speed.
- Each new particle is drawn as a 1-pixel cream square on the navy background, mirroring the palette of the gallery.
- Reset clears the canvas and restarts with a single seed.
Applications & Analogues
DLA-like growth appears in snowflakes, coral, lightning bolts, mineral dendrites, even urban growth models.