Deterministic Chaos
// The Double Pendulum
Two rods, two masses, no randomness whatsoever. The equations of motion are exact — and yet nobody can tell you where this pendulum will be in thirty seconds. Shift the starting angle by a hundred-thousandth of a radian and the paths diverge completely.
That is deterministic chaos: perfectly lawful, perfectly unpredictable. Same reason weather forecasts fade out after a week.
integrated with Runge–Kutta 4 · Δ shows the angular distance between the first and last clone
Lorenz found it by rounding 0.506127 to 0.506 in a weather model. Tiny input differences grow exponentially — the hallmark of a chaotic system.
Every frame follows Newton exactly. Chaos is not noise: it is sensitivity. Run the same start twice and you get the same motion, bit for bit.
The horizon past which prediction is useless. For this pendulum it is seconds, for the weather days, for the solar system millions of years.