Ants, birds and traders each follow local rules and respond to neighbors or feedback. Group patterns emerge with no leader, a process called self-organization.
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Feedback loops either stabilize or amplify change. When amplifying loops overpower stabilizing ones past a threshold, a system can shift abruptly into a new, often hard-to-reverse state.
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The butterfly effect is sensitive dependence on initial conditions: tiny differences in a deterministic system can grow into large ones. Lorenz found it in 1961 when rounding a number changed his simulated weather.
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Self-organized criticality is the tendency of some systems to drive themselves to a critical state without tuning. The sandpile model of 1987 was the first system shown to do this.
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