A billiard ball in a rectangle with two circular ends: slight changes in initial conditions make such a big difference that eventually it could be anywhere. To be precise, we say its motion is "ergodic".
For the precise definition of "ergodic" read my diary:
(link: https://tinyurl.com/baez-bunimovich) tinyurl.com/baez-bunimovich
great example of the evolution of apparent randomness from a completely deterministic process
Yes, it sort of demystifies how that works.
https://mobile.twitter.com/johncarlosbaez/status/1023252524248137728
see also https://plus.google.com/+johncbaez999/posts/cWQ3RYLCAoi