Double Pendulum Explorer

This is deterministic chaos, not randomness. Start two runs just 0.1° apart: after a while they no longer look related because separation grows roughly exponentially (a positive Lyapunov exponent). Energy keeps shuttling between the two arms through nonlinear coupling, so tiny phase differences get amplified into completely different future states. The equations are exact; what collapses is the prediction horizon.
:) This pendulum does not just go left-right; it keeps changing its mind about which arm leads the dance.

There is no motor, no noise generator, no trick — only two arms, two pivots, and gravity. The wild motion comes entirely from the second joint, which lets each arm push the other around. Try starting with a small nudge near the bottom: it swings almost like an ordinary pendulum. Chaos only takes over once you give it enough energy for the arms to swing over the top.
:) Complexity here is not built in; it is grown from something almost embarrassingly simple.

Release the pendulum from rest with the arms held out horizontally and watch the outer bob: for an instant it can accelerate downward faster than a freely dropped ball — more than g. The rigid arms act as a lever and whip, so the inner arm flings the outer one down harder than gravity alone ever could. It is the same effect that lets a hinged stick beat a falling coin to the floor.
:) Gravity starts the fall, but geometry decides who lands first.