Chaos theory studies deterministic systems whose behavior is effectively unpredictable due to extreme sensitivity to initial conditions. Edward Lorenz discovered this in 1963 while modeling weather: a rounding error of 0.000127 in initial conditions produced a completely different forecast. He called it the 'butterfly effect' — the idea that a butterfly flapping its wings in Brazil could set off a tornado in Texas.
Chaotic systems are everywhere: weather, turbulence, the three-body problem in astronomy, population dynamics in ecology, the beating of the heart. They share a remarkable property — they are fully deterministic (governed by precise equations) yet practically unpredictable beyond a short horizon. This is not randomness; it is something far more subtle.
These simulations let you explore the iconic systems of chaos theory: the Lorenz attractor, the logistic map's period-doubling route to chaos, the double pendulum, and the infinite complexity of the Mandelbrot set. Watch order dissolve into chaos and discover the deep mathematical structure hiding within apparent randomness.