The butterfly effect theory, a subset of the chaos theory, states that a small change at one place in a complex system can have catastrophic effects in another place. This is based on the idea of recurrence, which states the two main ingredients for chaotic motion are the approximate return of a system to its initial conditions and the dependency of the system on its initial conditions.
The behavior known as the butterfly effect can be seen in simple systems such as a ball placed on the crest of a hill with many different paths. Depending on slight differences in the initial conditions present when the ball is released, the ball may roll into any one of the paths.
Recurrence is the reason that complex systems, such as the weather, are difficult to predict due to the impossibility to measure the initial conditions of any storm accurately. It is due to this recognition of chaos that weather forecasters run multiple simulations with slightly different initial conditions and feature these scenarios as a consensus forecast.
The butterfly effect is also a common theme in fiction. This theme typically involves presenting multiple what-if scenarios when one story line diverges into two different outcomes because of a change in a minor event.