whatA snow crystal grows on the page from nothing but wandering molecules and one sticking rule: six arms, feathered with side branches, different every time.

whySnowflakes are the classic emergence. Nobody designs an arm, yet every flake is six-fold. The piece shows how a symmetry in the smallest rule, where a molecule may sit, becomes a symmetry you can see across the whole crystal.

howMolecules random-walk on a hexagonal lattice. When one touches the crystal it sticks readily at a tip and rarely in a bay, readily where the site lies along one of six axes and rarely between them, and a tip that has run ahead of the other arms sticks less until they catch up. Each accretion is drawn as a stroke along the bond it grew from. The six spokes at top right read the reach of each arm. Click to melt a patch and watch it regrow differently. When the flake reaches the rim it thaws, and a new one grows from the same seed.