In reply to wintertree:
> Frost patterns on roofs are amazing, they remind me of crystal patterns in a cross section of metal...
Same physics at work. The rate of advance of the crystal front (whether the crystal is growing into the melt, as in the metal, or into vapour, as happens in the ice crystals) is limited by how fast the latent heat of crystallisation can diffuse away. The boundary of the crystal is at the melting point, so there's a temperature gradient from there to the lower temperature of the environment, and it's this temperature gradient that drives the diffusion of the latent heat away. Imagine you start out with a flat interface, but a random fluctuation leads to some waviness. The bits of the crystal that stick out further then have a steeper temperature gradient next to them, so the latent heat diffuses away faster, so the waviness is amplified and you end up with fingers sticking out. The length scale selection comes about because very narrow fingers create too much interfacial area, and there's an energy penalty from the interfacial tension. Because this interfacial tension depends on the orientation relative to the crystal structure, the symmetry of the crystal is reflected in the relative growth rates in different directions, hence the hexagonal symmetry of the frost patterns.
Probably easier to explain with diagrams! (It's called a Mullins-Sekerka instability in the trade).
"Patterns in Nature, Why the Natural World Looks the Way it Does", by Philip Ball, is great on all this stuff.
https://www.philipball.co.uk/patterns-in-nature