Lorenz observed that minute differences in the initial conditions of his numerical models of the atmosphere could, after a relatively short time, lead to radically different outcomes. He realized that the differential equations used to describe atmospheric behaviour, while deterministic, were also highly dependent on initial conditions and that this limited the usefulness of practical weather forecasts to about a week. This phenomenon has become known as the butterfly effect, from the idea that the small air movement caused by a butterfly flapping its wings in one part of the globe could in theory result in a storm weeks later thousands of miles away.

He went on to investigate other examples of chaotic behaviour, establishing in 1963 that even very simple deterministic systems can show chaotic behaviour. One of his examples was the motion of a waterwheel, which, as he demonstrated, becomes unpredictable and prone to random reversals in direction when the rate of water flow exceeds a threshold value. In order to illustrate the chaotic dynamics of such systems, Lorenz devised the Lorenz attractor, a three-dimensional curve in which the location of a point represents the motion of a dynamical system in phase space. The curve shows how the motion of the system oscillates aperiodically between the two directions and never settles into a steady state.