Crystallization is a liquid-solid phase transition in which the solid grows by adding material from the liquid environment adjacent to it. This process, which can be classified as a type of spreading phenomenon, is complicated by the fact that there is a growth inhibition effect whereby the crystallization of a site inhibits the crystallization of nearby sites. The molecular causes of crystal growth inhibition, including interfacial surface tension and latent heat diffusion effects, can be incorporated in a detailed lattice model (see the Solidification CA) but it is also possible to use a very simple cellular automaton model (Packard, 1986) incorporating growth inhibition in a naive fashion, which produces patterns that bear a remarkable resemblance to the observed structures of snowflakes. We will develop this cellular automaton model for the formation of snowflakes on a hexagonal lattice.
KeywordsHexagonal Lattice Neighbor Site Cellular Automaton Model Liquid Environment Boolean Lattice
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- Packard, Norman H. “Lattice models for solidification and aggregation” Proceedings of the First International Symposium for Science on Form, Tsukuba University (1986). (Reprinted in Wolfram, Stephen. Theory and Applications of Cellular Automata. World Scientific (1986) pp. 305–310.)Google Scholar