Diffusion-limited solidification on a hexagonal lattice. A diffusion field drives growth; curvature and anisotropy determine branching morphology — reproducing snowflake-like patterns.
Parameters
Statistics
Solid cells 0
Steps 0
Crystal radius 0
Physics: Phase-field model φ(x,t) interpolates solid (φ=1) and liquid (φ=0). The Allen-Cahn equation:
τ∂φ/∂t = ∇²φ − φ(1−φ)(1−2φ)/ε² + κ(Δ + φ)
Anisotropy breaks 6-fold symmetry of hexagonal lattice into snowflake arms.