I had a request to run the butterfly effect simulations at a faster speed and for longer so we can observe more of the chaotic part of the simulation and look for convergences. As we can see, no convergences appear. This is expected since the trajectories of the balls aren't like two waves with differing frequencies or gears that will eventually come back into phase with each other given enough time. Bouncing balls in a circle are truly chaotic. Enjoy the fireworks!