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Browser Experiment Quantifies Chaos: Double Pendulum Diverges in Under 8 Seconds

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A developer used browser-based physics simulators to numerically measure chaotic behaviour in two classic systems: a double pendulum and the logistic map. Two simulated double pendulums released from positions just 0.057 degrees apart remained synchronised for roughly 5.6 seconds before fully diverging by 7.2 seconds. The calculated Lyapunov exponent of approximately 1.095 per second confirms exponential error growth, meaning any initial uncertainty doubles repeatedly until long-term prediction becomes impossible. The logistic map independently demonstrated the same universal route into chaos through period-doubling, with the ratio between successive doublings converging on the Feigenbaum constant of 4.669. Both systems are fully deterministic, highlighting that chaos arises not from randomness but from extreme sensitivity to initial conditions.

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