How to demonstrate Chaotic Behaviour

Question

Hello everyone!

For a seminar on Chaos Theory, I am going through Strogatz's 'Nonlinear Dynamics and Chaos', holding a talk every week for the prof and PhD students. It's absolutely awesome, and I would like to end the semester with a bang to thank them.

Do you know of any fun demonstrations of chaotic systems that I could put together? My best idea so far is programming some lesser known strange attractors and demonstrate how they form over time. However, it would be even cooler to present something from the real world.

Any ideas appreciated!

Answer 1

Conway's Life is a classic. It's simple, but full of emergent properties.

Alternatively, a demonstration of The Gambler's Ruin is more mathy, and might prompt more serious thought than wonder.

Answer 2

A double pendulum.

Answer 3

Here’s a really interesting problem from my field (Control Theory).

Take a game of billiards. We have a cue ball and we want to make the 9 ball into any pocket. Anyone with a decent amount of practice could make this , ignoring some difficult positions.

For simplicity sakes, suppose we have a perfect line between the cue ball, the 9 ball, and the pocket. If you hit the cue ball at a sufficiently center position, you’ll make it.

Now consider a ball between the cue and the 9 ball. You have to hit this ball into the cue to go into the pocket. It’s a bit harder but still doable. Let’s add ANOTHER ball now. Suddenly the difficult increases tremendously, but it’s still possible.

It turns out that with as little as three balls between the cue and the 9 ball, EVEN if they’re aligned in a straight line, the system is increasingly chaotic subject to small perturbations from the initial point of contact with pool stick.