Fueling Innovation and Discovery The Mathematical Sciences in the 21st Century (2012) / Chapter Skim
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Cellular Automata / Sublimely Complex
Cellular Automata / Sublimely Complex
Pages 36-39
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From page 36... ...
A snowflake grows by attaching one molecule of water at a time. How does that process lead to the lacy, frilly shapes that we see in real snowflakes?
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From page 37... ...
A cascade of toppling grains is thereby produced that can continue 13 / A "snowfake" grows on a hexagonal grid by using simple attachment rules that model the adhesion of water molecules to a growing ice crystal. The resulting model (left, reprinted with permission from Janko Gravner, UC Davis, and David Griffeath, University of Wisconsin)
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From page 38... ...
Another beautiful and conceptually important cellular automaton is called the "rotor router." One version was designed to mimic internal diffusion-limited aggregation, which is more or less the flip side of snowflake growth. Imagine a crystal that instead of growing by attachment of particles from outside, grows by attachment of new particles from within.
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From page 39... ...
And there seems to be an intermediate and remarkably structured regime between freely moving streets and gridlock that could be described as a moving traffic jam whose existence has not yet been confirmed. Though much remains unknown about cellular automata, it is exactly at such wild and untamed frontiers that the mathematical sciences grow.
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