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Eternal Struggle

(yoavg.github.io)
675 points yurivish | 6 comments | 31 Aug 25 19:04 UTC | HN request time: 0.217s | source | bottom
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MrJohz ◴[31 Aug 25 20:26 UTC] No.45086773[source]▶
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.
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1. SonOfLilit ◴[31 Aug 25 20:49 UTC] No.45086951[source]▶
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.
replies(4): >>45087148 #>>45087151 #>>45087219 #>>45088905 #
2. istjohn ◴[31 Aug 25 21:13 UTC] No.45087148[source]▶
Yes, because it's not actually area that balances out but mean time between bounce against the black/white boundary.
3. n2d4 ◴[31 Aug 25 21:14 UTC] No.45087151[source]▶
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.)

4. ◴[31 Aug 25 21:22 UTC] No.45087219[source]▶
replies(1): >>45087532 #
5. ◴[31 Aug 25 22:05 UTC] No.45087532[source]▶
6. aoeusnth1 ◴[01 Sep 25 02:32 UTC] No.45088905[source]▶
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.