This demo shows how very small changes in initial conditions can make for a very different behaviour of the system in a very short time; thus making it a chaotic system.
The demo starts with 2 double pendulums; one green and one blue using nearly the same initial conditions, one pendulum has one of its starting angles changed by ε (default is 1/10,000) even with that small of a change the different pendulums will start to diverge after about 5-7 seconds.
You can manipulate all values in real time.
A demo used to develop and test NDSolve the numerical ODE solver used to integrate the equations of motion for a double pendulum system in real-time
can be seen at this link.
More information about the math and equations of motion can be found on Wikipedia and Wolfram science world.
Can be found on my GitHub.