Dendritic crystal growth via phase-field cellular automaton with hexagonal symmetry
Ice grows as a crystal with six-fold symmetry from hexagonal lattice geometry. The phase-field model tracks a continuous order parameter φ (0=liquid, 1=solid).
Supercooling drives solidification — latent heat released at the interface must diffuse away. The Mullins-Sekerka instability: a bump on the solid front grows faster (better heat removal), causing dendritic branching.
Anisotropy in surface tension selects six preferred growth directions, creating the classic snowflake shape.