The "Butterfly Effect" is the propensity of a system to be sensitive to initial conditions.Such systems over time become unpredictable,this idea gave rise to the notion of a butterfly flapping it's wings in one area of the world, causing a tornado or some such weather event to occur in another remote area of the world.
Comparing this effect to the domino effect, is slightly misleading.There is dependence on the initial sensitivity, but whereas a simple linear row of dominoes would cause one event to initiate another similar one, the butterfly effect amplifies the condition upon each iteration.
The butterfly effect has been most commonly associated with the Weather system as this is where the discovery of "non-linear" phenomenon began when Edward Lorenz found anomalies in computer models of the weather. But Henri Poincaré had already made inroads into this area. Mapping the results in "phase space" produced a two-lobe map called the Lorenz Attractor. The word attractor meaning that events tended to be attracted towards the two lobes,and events outside of the lobes are such things like snow in the desert.
Following are a couple of diagrams of the dual-lobed "Lorenz attractor" that help illustrate the theory, as it looks like a butterfly.
