This is one of the clearest definitions of a chaotic system that I’ve seen. I really like the timescale comparisons: seconds for pendulums, days for weather, Myrs for the solar system.
I’d love to see an XKCD table of timescales of various chaotic systems. 🙂 This is close but not quite: https://xkcd.com/1399/
Originally shared by Larry Phillips
A double pendulum is a pendulum with another pendulum attached to its end. It is one of the simplest systems that can have chaotic behavior.
This animation shows the calculated movement of two double pendulums that start from slightly different initial conditions. After a short time, the motion predicted for each of them is completely different. This is the hallmark of a chaotic system – differences in initial conditions, however small, eventually result in large differences in the system behavior.
Note that the mathematical model for the double pendulum is exact, and there is no inherent randomness in the motion. It’s just that we can never know the initial conditions precisely, so that the predicted motion will become less and less certain as we go further out in time.
Two examples of chaotic systems are
1) the Solar System, on a time scale of about 100 million years, and
2) the weather, on a time scale of around 12 days
Animation source: goo.gl/vspShs