Crystal Growth: Diffusion-Limited Aggregation (2D)

Growth Conditions

Supersaturation 1.00×

Temperature (diffusion) 3.0

Sticking probability 0.35

Nucleation seeds 3

Live Readout

Elapsed time

0.0 s

Attached atoms

Cluster radius

0 px

Growth rate

0 /s

How it works

This is a 2D diffusion-limited aggregation (DLA) model — the Witten–Sander process used to explain how many real mineral deposits, frost and metal electrodeposits grow. Particles representing dissolved SiO₂ are released at a spawn ring and perform a random walk (Brownian motion) driven by the Temperature slider. The instant a wandering particle touches the existing cluster it attaches with probability set by Sticking probability — otherwise it keeps wandering and may try again later.

High sticking (≈1.0) — a particle freezes on first contact, so the cluster grows an open, branching, fractal habit (classic DLA, dimension ≈1.7 in 2D) — the kinetically-limited regime.
Low sticking — particles bounce and explore the surface before attaching, filling in gaps and producing a denser, more compact, faceted mass closer to how a real slow-grown amethyst crystal fills a cavity.
Supersaturation sets how many new particles enter the system per second — the dissolved-mineral concentration driving growth.
Nucleation seeds — real amethyst geodes rarely grow from a single point; multiple seed crystals compete for the same supply of dissolved silica, exactly as the multi-seed option shows.

Color variation across the cluster mimics the natural Fe³⁺ trace-impurity zoning that gives amethyst its purple banding.

Attached crystal (SiO₂ + Fe³⁺) Diffusing particle