Frost on a window is a fractal caught between one and two dimensions
The fern-like patterns frost paints on a cold window are fractals. Because the ice crystals can only spread across a flat pane, the patterns have a fractal dimension between one and two, whereas a snowflake, growing freely in the air, exceeds two. Frost usually skips the liquid stage entirely, turning vapour straight into ice.
Air holds more water vapour when warm than when cold. If a surface chills air below its frost point, the excess vapour deposits directly as solid ice, a process called desublimation, and seed crystals grow into needles, tree-like branches, blades or snowflake shapes depending on temperature, turbulence, humidity and surface texture. If water condenses as liquid first and then freezes, the result is icing instead, a glassy coating rather than spiky crystals. Glass attracts water vapour well, which is why a car's windows often frost before its paintwork.
Frost usually needs a surface colder than the surrounding air. That explains frost ringing cracks in a wooden boardwalk where humid air escapes from warmer ground below, and frost gathering on the heads of rusty nails, since dark metal radiates heat efficiently. On calm nights cold air slides downhill into hollows, so frost can coat a valley floor while the air a few feet higher stays above freezing, producing patchy frost between neighbouring fields.
Hoar frost, the white crystals that form on clear, still nights as heat escapes to space, takes its name from an Old English word for looking old, because it makes trees seem white-haired. It comes in several varieties: air hoar on branches and wires, surface hoar on snow, crevasse hoar inside glaciers and depth hoar, large stepped crystals growing in cavities under dry snow. Surface hoar can be dangerous. When fresh snow falls on its furry crystals, the new layer bonds poorly, setting up avalanches. In parts of Antarctica, wind-broken hoar crystals roll into balls called yukimarimo, rather like dust bunnies.
Other types include advection frost, tiny spikes built by bitterly cold wind, usually growing into it; black frost, cold enough to harm plants yet producing no visible ice; and white frost, which needs humidity above 90 percent and temperatures below minus 8 degrees Celsius. Crops from warm climates suffer when water inside their cells freezes, so farmers in frost-prone areas invest heavily in protection.
Source: Frost
