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If one examines the following image:

enter image description here

One will notice that the ice is freezing in this characteristic criss-cross pattern. Are there any theories to explain this behavior? I've seen this on car wind-shields as well. I thought the crystalline structure of ice was a hexagonal ring: shouldn't the ice freeze in some sort of six-directional pattern?

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  • $\begingroup$ I believe John Rennie is correct. If you are looking for theories that can explain structure formation in nature, including crystallization, then you will have to learn about phase transitions and look into synergetics as developed by Hermann Haken's group. There are general mathematical procedures to treat certain types of systems that form in near non-equilibrium conditions but have not developed fully chaotic dynamics, yet. $\endgroup$ – CuriousOne Dec 26 '15 at 22:04
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The ice crystals are nucleating in tiny scratches in the glass. The pattern you see isn't due to single crystals growing outwards in an approximate grid. It's many individual tiny crystals nucleating separately along a scratch line.

The tiny scratches are presumably caused by you washing the mirror, and their relative orientation is down to the scrubbing motion you use.

This is of course just a hypothesis since I can't inspect your car mirror in detail. You can check whether I'm correct by examining the ice with a magnifying glass to confirm that you're seeing tiny clusters of unrelated crystals. Also melt the ice with a hair dryer (so it dries off the water left by melting) and you should be able to make out the underlying scratch.

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