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.

It doesn't. It quickly just becomes a random curve after a few minutes at normal speed if you leave it open.

For obvious reasons it tends to stay half white half black (if one half gets smaller its ball will bounce faster) but the shape and its orientation varies randomly.

Off the top of my head, there is no mechanism for tension, so it would basically approach a random curve with equal white and black areas over time, but in addition there is the point reassignment function which acts as a kind of low pass filter so you get something that looks like a sinusoid?

I think it’s just random chance. I haven’t run any simulations or anything, but I suspect the YY curve is no more stable than any simple 50-50 split. I bet over large timespans the YY curve straightens out just from entropy.

It doesn't. Seems to be like a lava lamp until one ball breaks thru. See the other comment with the console command to edit the speed.