Crystal Genesis: Diffusion-Limited Crystal Growth (2D)

Growth Conditions

Sticking probability (η) 0.50

Particle mobility (temperature) 1.40×

Active solute walkers 24

Nucleation sites 1

Live Readout

Cluster mass (N)

Cluster radius

0.0

Radius of gyration

0.0

Fractal dimension

—

Simulated steps

Active walkers

How it works

This is a diffusion-limited-aggregation (DLA / Witten–Sander) model of crystal growth. One or more seed nuclei sit at the centre of a supersaturated field. Solute particles are launched from a ring around the growing crystal and perform an unbiased random walk (Brownian motion) — a discrete approximation of diffusion:

x(t+dt) = x(t) + m·ξx·dt
y(t+dt) = y(t) + m·ξy·dt
ξx, ξy ~ Uniform(−1, 1)   (m = mobility slider)

When a walker's random path brings it within one lattice spacing of the existing cluster, it sticks with probability η (the "sticking probability" slider) — modelling how readily an arriving particle is captured into the crystal lattice versus re-diffusing past it. A walker that wanders past a kill radius is recycled back onto the launch ring, conserving the total particle budget set by the "active solute walkers" slider.

η → 1 (fast attachment): particles freeze on first contact, screening the tips and starving the cracks — this produces open, branching, fractal dendrites, the classic DLA result with dimension D ≈ 1.7 in 2D.
η → 0 (slow attachment): particles have many chances to explore before sticking, filling in gaps — this produces denser, more compact, more isotropic crystal habit, trending toward D → 2.
Mobility raises the effective diffusion rate (temperature), speeding up growth without changing its geometry.
Fractal dimension is estimated live from the mass–radius scaling law N ∝ R^D, i.e. D = ln(N)/ln(R), the standard way DLA clusters are characterised experimentally and numerically.

Crystal lattice (stuck) Diffusing solute walker Nucleation seed

Cluster complete — press Reseed to regrow