A graph of a chaotic function called the Lorenz attractor.

If these two connected pendulums started in a position that was even a little bit different, the gray line would look completely different.

Chaos theory is a part of mathematics. It looks at certain systems that are very sensitive. A very small change may make the system behave completely differently.

Very small changes in the starting position of a chaotic system make a big difference after a while. This is why even large computers cannot tell the weather for more than a few days in the future. Even if the weather was perfectly measured, a small change or error will make the prediction completely wrong. Since even a butterfly flapping its wings can make enough wind to change weather, a chaotic system is sometimes called the "butterfly effect". No computer knows enough to tell how the small wind will change the weather.