one expects that during the growth of a particular snowflake there should be alternation between tree-like and faceted shapes, as new branches grow but then collide with each other.

And if one looks at real snowflakes, there is every indication that this is exactly what happens. And in fact, in general the simple cellular automaton shown below seems remarkably successful at reproducing all sorts of obvious features of snowflake growth. But inevitably there are many details that it does not capture. And indeed some of the photographs on the facing page do not in the end look much like patterns produced at any step in the evolution shown below.

The evolution of a cellular automaton in which each cell on a hexagonal grid becomes black whenever exactly one of its neighbors was black on the step before. This rule captures the basic growth inhibition effect that occurs in snowflakes. The resulting patterns obtained at different steps look remarkably similar to many real snowflakes.

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From Stephen Wolfram: A New Kind of Science [citation]