Chaos is a state of apparent disorder and irregularity whose evolution in time, though governed by simple and exact laws, is highly sensitive to starting conditions. Small variations in these conditions produce widely different results, in such a way that the long term behaviour of chaotic systems cannot be predicted.
It is impossible to accurately predict the motion or progression through time of even a simple chaotic system – herein lies the beauty of the double pendulum. Compared to real world systems such as the weather; molecular vibrations; fluid dynamics; or solar systems and galaxies, it is an extremely simple system which can be easily modelled and understood mathematically. However, unlike a simple single pendulum, it is impossible to predict the long term behaviour of the double pendulum.