Eternal Struggle

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.

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.

Yes, because it's not actually area that balances out but mean time between bounce against the black/white boundary.

Now the question remains, are there stableish equilibria that are 50/50? Splitting it into two half-circles sounds like an equilibrium at first glance, but I'm not convinced it is, as only a tiny bit of random luck seems to make it become a "horseshoe" pattern instead.

(That assumes that the simulation is randomized of course, which doesn't seem to be the case for the one in the link posted here.)

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.

I think the balls stop when the tab isn't focused

That's in another two months.

That's not a stable equilibrium if the hits have a large enough effect with respect to the movement of the balls. The internal circle will create disturbances against both sides of the inner circle, but the outer ball will have to travel a longer distance to move from one side to the other to counter them.

Yeah, definitely run it in the foreground. Mine became completely black in about 3 hours.

But you can say the same thing about a circle with a straight line as separator.

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.

All models are wrong…

But some are useful.

Me too. Does black always win? If so, why?