Category: Physics

Summary: Mapping how external drift changes the fractal dimension of diffusion-limited aggregation clusters.

Diffusion-limited aggregation normally grows ramified fractal clusters in two dimensions, but a directional drift biases walkers and can turn that branching growth into thinner, more needle-like structures. This experiment asks where that crossover becomes sharp and how the characteristic drift scale changes with cluster size.

The simulation generates DLA clusters over a range of drift strengths and sizes, then estimates the fractal dimension and extracts a crossover velocity where the geometry drops away from its undrifted value. By repeating that across sizes, it tests a scaling law for how sensitive larger clusters are to directional bias.

That produces a phase-diagram style view of how transport bias competes with diffusion in aggregate growth. The value is not just the limiting fractal dimensions, but the size-dependent route between them.

Method: Repeated DLA simulations with biased random walks across drift strengths and cluster sizes, followed by fractal-dimension and crossover-scale estimation.

What is measured: Fractal dimension versus drift, crossover drift scale, scaling exponent for the crossover, and size dependence of cluster geometry.