Drag to rotate. Scroll, pinch, or use the Zoom buttons to zoom. Double-click resets the view. Two trajectories, A in yellow and B in magenta, start a tiny gap apart. For a while they trace the same path, then the gap grows roughly tenfold every couple of time units until they end up on different wings. That's the sensitivity to initial conditions Edward Lorenz stumbled on in 1963, when he restarted a weather run from rounded-off numbers.

Try ρ. Below 1 everything falls to the origin. Up to about 24.74 the orbits spiral into one of two fixed points at the centers of the wings (around 24 they wander chaotically for a while first). Above that, the butterfly. At large values like 99.96 the chaos gives way to a periodic loop.

Integrated with fourth-order Runge–Kutta at dt = 0.005. Companions: the Tek 4006 cobweb plot and the green scope clock.

Sharing a view. The page's address keeps your current settings, zoom and viewing angle. Press Copy link and anyone who opens it sees the same thing.