[thejohnconway]

People are responding to you saying that it doesn't retain the yin-yang shape, but I've been watching for a while on 64x speed, and the yin-yang shape is one it repeatedly returns to.

I'm not even a dimwitted individual with an advanced degree in hyperbolic topology, but I can see what's happening intuitively. When one of the balls makes an indent large enough, that indent focusses the bounce from the circular edge which reinforces the indent further. This leads to a semi-stable shape where one of the balls is bouncing around a horseshoe and the other in a tunnel. However, if one side of the horseshoe becomes pinched small enough that ball is less likely to enter, that side of get eliminated, and you have a yin-yang.

More simply, the round edge seems to encourage tunnelling, and any asymmetry in the tunnelling is yin-yang-ish.