Edward Norton Lorenz in the context of "Initial conditions"

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972. He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.

The Lorenz system is a three-dimensional classical dynamic system represented by three ordinary differential equations . It was first developed by the meteorologist Edward Lorenz and describes chaotic behavior of fluid movement when subjected to heating.

Although the Lorenz system is deterministic, its dynamics depend on the choice of initial parameters. For some ranges of parameters, the system is predictable as trajectories settle into fixed points or simple periodic orbits. In contrast, for other parameter ranges, the system becomes chaotic and the solutions never settle down but instead trace out the butterfly-shaped Lorenz attractor, popularly known as butterfly effect. In this regime, small differences in initial conditions grows exponentially making long-term prediction practically impossible.