The proverbial wing beat of a butterfly, which triggers a tornado is an allegory for chaotic systems, where the smallest of changes in intitial conditions can cause great long term changes. In physics there are many systems which display such behaviour. These are sometimes incredibly simple. Even a pendulum hung on another pendulum (a double pendulum) shows such behaviour.
In the animation you can experiment with a simple double pendulum and observe the trajectory of the erratically moving spots. It is possible to vary the length of the pendulums and the direction and strength of the applied gravity.