Ice Crystal Formation: Diffusion-Limited Hexagonal Growth (2D)

Vapor Field

Ambient vapor density (α) 0.40

Attachment rate (β) 0.035

Diffusion rate (γ) 0.55

Growth speed 1.0x

Live Readout

Ticks elapsed

Frozen cells

Crystal radius

Active front

How it works

This is a Reiter-style local cellular automaton for snow-crystal growth, run on a hexagonal lattice (not a decorative branch-mirror like the 3D version — every hexagon is an independent cell obeying the same three rules, and the six-fold symmetry you see is emergent from the lattice geometry, not enforced). Each unfrozen cell carries a water-vapor mass; each tick:

boundary(x) = x unfrozen AND touches a frozen neighbor
diffuse:  m'(x) = m(x)(1-γ) + γ · mean(m(neighbors))
attach:   if boundary(x): m'(x) += β
freeze:   if m'(x) ≥ 1: x becomes frozen permanently
refill:   outer-ring unfrozen cells reset toward α (ambient supply)

α sets how much vapor is available at the domain edge (more α = faster, denser growth). β is how fast mass accumulates once a cell touches ice — high β outruns diffusion and fills in solid hexagonal plates; low β leaves boundary cells starved, so only the tips that reach fresh vapor first race ahead, producing sharp dendritic branching (the same tip-instability mechanism behind real frost and snowflake arms). γ controls how fast vapor spreads before freezing — low γ starves everything but the outermost tips (needles); high γ smooths the field so growth stays compact (plates).

Bright cells — frozen ice, shaded by the vapor mass they froze with.
Faint blue haze — the live diffusing vapor field feeding the crystal.
Active front — unfrozen cells currently touching ice, i.e. where growth can happen next tick.

Frozen ice Diffusing vapor Active growth front