The cool thing about this is that it's self-balancing - if either side gets larger than the other due to random chance, the ball in that side will have more space to bounce in, and therefore bounce less often, slowing its growth. Meanwhile, the ball in the smaller side will bounce more often in its smaller space, making up the ground.
It seems there is a parallel with physics: two pressurized chambers with equal pressure and a membrane separating them. The odd thing here is that there is only one molecule in each of them.
It's amazing how stable it is. It's been running in a background tab for a hour now, and it still has the yin/yang look.
But you can say the same thing about a circle with a straight line as separator.
There are stableish equilibria that are not 50-50, e.g. one color having a donut around the other color that has a donut hole.