Fall
A snow crystal growing as it falls. The six arms never touch and never compare notes; they match because they fell through the same air at the same moments. Your hand is that air. Hold anywhere and the air turns humid, and the arms broaden into plates. Let go and the tips thin and branch again. There is no chance anywhere in it, so the crystal is a record of its weather and of nothing else, and you can keep it.
what the crystal can say about itself
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Ukichiro Nakaya, who grew the first artificial snow crystals in Sapporo in 1936, called a snow crystal a letter from the sky: its form is a record of the air it fell through, and he could read the temperature and the humidity back out of a shape. This piece takes the sentence at its word. The line above is the letter. It is a list of how long the air was dry, then humid, then dry, counted in blocks of thirty-two steps. Put in a link, it regrows the same crystal on any machine, to the last bit, because the solver adds, subtracts, multiplies and divides and does nothing else.
The model is Clifford Reiter's, from 2005. Every cell of a hexagonal lattice holds an amount of water. Ice is any cell holding one or more. Vapor diffuses between the cells that are not ice and do not touch ice; cells at the boundary of the crystal keep what reaches them, and take a little more each step from the air above and below the plane. That little more is the humidity your hand controls. When it is small, growth is starved and goes to whatever sticks out farthest, so corners run away into arms and arms into side branches. When it is large, everything at the boundary fills at once and the arms close into plates.
Only one twelfth of the crystal is computed. The other eleven are its mirror images, which is not a shortcut around the physics but the physics: nothing the arms could tell each other would travel faster than the weather they share. A reference solver that stores every cell and uses no symmetry agrees with the twelfth to fifteen digits.
The picture is drawn the way snow is photographed, in dark field, where flat ice is nearly black and only edges and ridges send light to the lens. The brightness is the slope of the ice's own thickness, so the faint ribs inside a plate are real to the model: they are the places where growth slowed. The pale haze is the vapor, and the dark margin hugging the arms is where the crystal has already drunk it.
What this is not. It is flat, so it cannot choose between plates and columns the way real snow does with temperature. It has no surface physics: its rules were chosen because they give believable shapes, not derived from how water molecules attach to ice. Gravner and Griffeath's 2008 model is the more honest rung and is not what runs here. What this one keeps is small and true: growth that is limited by diffusion favors what sticks out, more water fills it back in, and the same history gives the same arms.
Eight checks and five guesses were written down before the solver existed, and run blind. Water is conserved through freezing to thirteen digits. A drop of vapor spreads by exactly half a cell squared per step. With no vapor at all the crystal is a perfect hexagon that gains a ring every sixty-four steps, to the step. A recorded weather regrows its crystal byte for byte. One check failed as first written, and the fault was the examiner's: its test crystal ran into the edge of its small lattice. The amended run is the one reported. The five guesses were about how the model behaves (dry air branches, humid air fills, a hold is visible in the ice), and all five held.
Keeping a crystal saves it at 2,400 pixels with its weather printed beneath it. The print is its own provenance: the line on it is enough to grow it again.
lattice radius 360 cells · landing at 302 · 389,881 cells in all, 32,761 computed