Why in a probabalistic structure like a very well-formed snowflake is there so much symmetry between arms (and most especially the mirror symmetry on each arm) between areas that are millions or billions of atoms away from each other?
So this turns out to be a really cool question. Part of what makes snowflakes unique is that each one is grown in a slightly different environment, and over the course of the growth of a snowflake this has a startlingly big impact. There are some cool attempts to model this with nonlinear systems / differential equations, and it does seem to be the case that if you have uniform growth conditions, you can get really different looking snowflakes that are still symmetrical.
So this turns out to be a really cool question. Part of what makes snowflakes unique is that each one is grown in a slightly different environment, and over the course of the growth of a snowflake this has a startlingly big impact. There are some cool attempts to model this with nonlinear systems / differential equations, and it does seem to be the case that if you have uniform growth conditions, you can get really different looking snowflakes that are still symmetrical.