The Growth of Crystals
At a microscopic level crystals consist of regular arrays of atoms laid out much like the cells in a cellular automaton. A crystal forms when a liquid or gas is cooled below its freezing point. Crystals always start from a seed--often a foreign object such as a grain of dust--and then grow by progressively adding more atoms to their surface.
As an idealization of this process, one can consider a cellular automaton in which black cells represent regions of solid and white cells represent regions of liquid or gas. If one assumes that any cell which is adjacent to a black cell will itself become black on the next step, then one gets the patterns of growth shown below.
