In the winter of 1961, Edward Lorenz, then working on weather prediction at MIT, wanted to re-run a simulation on the Royal McBee LGP-30 computer on his desk a bit faster. Typing in by hand the value 0.506127 from an earlier printout, he truncated it to 0.506; within simulated minutes the tiny difference had produced a completely different weather pattern. Lorenz realised this was not a computational error but a property of the model itself — what is now called sensitive dependence on initial conditions.

His 1963 paper in the Journal of the Atmospheric Sciences, "Deterministic Nonperiodic Flow," laid this behaviour bare with a remarkably simple system of three equations. The solutions wandered through phase space without ever crossing themselves and without ever repeating, yet stayed inside a bounded region — a two-winged geometry that became known as the Lorenz attractor. Beside the fatalism of determinism and the anarchy of randomness, a third category was born: systems whose rules are exact but whose behaviour is, in practice, unpredictable.

In 1972 Lorenz gave a talk to the American Association for the Advancement of Science with a title that fixed the idea in everyday language: "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" The butterfly effect metaphor, joined by Benoît Mandelbrot's fractal geometry in 1975, Mitchell Feigenbaum's universal constants of period doubling in the mid-1970s, and James Yorke's popularisation of the word "chaos" around the same time, became the seed of a new field.

Chaos theory not only set a mathematical limit on weather forecasting but also gave a shared language for sudden ecological collapses, cardiac arrhythmias, fluid turbulence, financial markets, and the long-term instability of planetary orbits. The clockwork universe of Newton gave way to a nature that is faithful to its own equations and yet, in the long run, unforeseeable.