Many complex systems - from immensely complicated ecosystems to minute assemblages of molecules - surprise us with their simple behaviour. Consider, for instance, the snowflake, in which a great number of water molecules arrange themselves in patterns with six-way symmetry. How is it that molecules moving seemingly at random become organized according to the simple, six-fold rule? How do the comings, goings, meetings and eatings of individual animals add up to the simple dynamics of ecosystem populations? More generally, how does complex and seemingly capricious micro-behaviour generate stable, predictable macro-behaviour?
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