Brownian Crystallisation (Diffusion-Limited Aggregation)
Stochastic simulation of crystallisation via Brownian motion and irreversible aggregation (DLA).
Demo clip of the simulation output (poster shown before playback).
Overview
This project investigates Brownian crystallisation using a diffusion-limited aggregation (DLA) model. Particles undergo random walks on a 2D lattice and irreversibly bind on contact with a growing cluster, producing emergent crystalline and fractal-like structures.
The goal is to show how simple stochastic rules at the microscopic level generate complex macroscopic morphology.
Physical model
Core rules
- Particles perform discrete 2D Brownian motion (random walk)
- Motion occurs on a finite square lattice
- Particles stick irreversibly upon first contact with the aggregate
- The aggregate acts as a growing absorbing boundary
DLA is a minimal model for diffusion-dominated pattern formation, relevant to crystal growth, electrodeposition, corrosion, and colloidal aggregation.
Implementation
Simulation
- Monte Carlo random-walk simulation
- Efficient state updates with vectorized NumPy operations
- Explicit tracking of aggregate geometry over time
Visualization
- Frame-by-frame rendering of the evolving cluster
- Animation generation for qualitative inspection
- Parameters exposed for morphology exploration (density, lattice size, release radius)
Key observations
- Growth becomes anisotropic despite isotropic diffusion
- Branching emerges naturally from screening and stochasticity
- Morphology is sensitive to particle density and domain size
- The cluster exhibits fractal-like geometry
Why this matters
This is a clean example of non-equilibrium structure formation: macroscopic order and complexity emerging from simple, local probabilistic rules. The same modeling mindset applies across physics, materials, and complex systems.