What is the butterfly effect?

The butterfly effect means tiny changes in initial conditions produce completely different outcomes. In this simulator two pendulums start just 0.001 radians apart but after 20 seconds they swing in totally different directions. This is why long-term weather prediction is fundamentally limited.

Why do the two pendulums diverge?

The combination of nonlinear gravity, damping, and periodic driving creates chaos. Each pendulum follows deterministic equations but the exponential amplification of tiny differences means their paths quickly become uncorrelated. Remove the drive force and they stay synchronized.

Two Chaotic Pendulums — Butterfly Effect Simulator

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Two Chaotic Pendulums