Chaos Theory is the name given to a branch of physics and mathematics studying systems that are extremely sensitive to starting conditions. A chaotic system is one where a very small difference, or error, in initial circumstances gives very different outcomes. In the applied sciences, such systems are typically impossible to predict in the long term. An example of a chaotic system would be weather forecasting, where short term predictions are possible, but long term predictions are useless. Chaos theory is often termed the "Butterfly Effect", as a lecture by Edward Lorenz, an important figure in the theory, titled a lecture on the subject "Does the flap of a butterfly's wings in Brazil cause a tornado in Texas?".
A simplified example of a chaotic system would be one where the initial input is one decimal value. Each tick, the value is multiplied by ten, and the unit digit is removed. If, for example, the original value was 4.198334, the system would go:
If, however the original value was different, perhaps due to a rounding error, or error in measurement, the initial value could be 4.198335. The system would then go
Each tick, the error affects the result more strongly. This large change in results from a small change in initial values is an example of a chaotic system.