whatA thousand double pendulums swing together, identical except for a millionth of a radian between neighbours, and only their second bobs are drawn. For a while they move as one stroke of ink. Then, at a moment the clock marks, the stroke frays, fans, and explodes into a butterfly of a thousand separate fates. Click to start again; the further right you click, the larger the seed difference and the sooner the horizon.

whyThis is deterministic chaos made visible: no randomness enters after the start, yet prediction fails on schedule. The spread between the pendulums grows exponentially, so the sparkline of its logarithm climbs as a straight line, and the horizon moves only gently when the seed difference shrinks a thousandfold. Weather forecasts die at the same kind of wall.

howEach pendulum is two rods and two bobs under gravity, integrated with fixed-step Runge-Kutta, and pendulum number i starts with its second angle offset by i millionths of a radian. Nothing else differs and nothing random happens after that. The piece draws each second bob's recent path as a fading line. The readout tracks the fan's angular width; when it passes ten degrees the clock freezes: that is the Lyapunov horizon. When the butterfly has fully mixed, a new stroke begins from a fresh seeded pose. One integer seeds the pose; your click sets the perturbation.