Chaos simulation: wacky double pendulum.

Chaos is all around us. Except chaos in physics doesn't have the colloquial meaning of complete disorder. Instead, it means the system's behavior is extremely sensitive to even the tiniest disturbances, also known as the butterfly effect. Here is a simulation of a simple chaotic system. Click anywhere to make nearly identical copies and see how the synchronization breaks within just a short time. Click again to throw away the copies. 

You can see that you really don't need it to be complicated to see the wackiness of chaos, just two balls on springs will do. Pretty much any physical system with three or more objects is chaotic, let alone something like, say, the Earth's weather system. That's why, no matter how powerful our supercomputers get it will never be possible to predict the weather for more than about a couple of weeks in advance - unless we learn how to actively control it that is.