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The science
Reiter's hexagonal cellular automaton
Snow crystals grow when water vapour diffuses to the ice surface and attaches there. The model keeps one vapour mass s per hexagonal cell. A cell is receptive if it is frozen or touches a frozen cell. Every step the non-receptive mass u diffuses and the receptive mass v stays put: st+1 = v + u + (α/2)(⟨u⟩neighbours − u) + γ [receptive]. A cell freezes once s ≥ 1. The rim of the box is held at the background vapour level β.
The three parameters play the roles of diffusion speed (α), humidity (β) and the extra vapour deposited on the crystal (γ, a stand-in for attachment kinetics and surface melting). Large β fills the plate, small β leaves branches; the six arms exist because the lattice has six-fold symmetry and the tips shield the vapour from the sides (diffusion-limited growth, Mullins-Sekerka instability).
Honest simplifications
Real snow crystals depend on temperature (plates near -2 C, needles near -5 C, plates again near -15 C) through anisotropic surface kinetics; this model only reproduces the diffusion-limited branching qualitatively and is not calibrated in kelvin. The 3D page is a decorative render; this page is the actual lattice model.
What to try
- Start with Stellar plate, then lower beta in small steps: the plate sprouts arms and then side branches.
- Click on the field to add extra seeds and see two crystals compete for the same vapour.
- Watch the vapour profile (graph 2): it drops below the freezing level in front of the tips, which is why tips grow fastest.