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Eternal Struggle

yoavg.github.io

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Re: Eternal Struggle

#91

Post by thejohnconway »

federico-peconi wrote: post #30

so simple yet so deep! anyone willing to provide a math-proof like argument on why the shape seem to stick to the YY curve indefinitely as the "eternal" name suggests? Should it always be this way or is there at least one bad initial bouncing configuration for which chaos can take place and we loose the YY curve? Does not seem that obvious to me.

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.

Re: Eternal Struggle

#93

Post by raspasov »

wvbdmp wrote: post #61
francisduvivier wrote: post #60

Some people here were asking for it so I quickly vibe forked a speed control slider for farming some karma here on Hacker News: https://francisduvivier.github.io/eternal-struggle-with-spee... Code: https://github.com/francisduvivier/eternal-struggle-with-spe...

Not to alarm anyone, but when I ran this, the black ball eventually joined the dark side and the whole thing ended up black. I’m sure this doesn’t mean anything for the greater universe.

The opposite can also happen (where the whole thing goes white).

Re: Eternal Struggle

#95

Post by [deleted] »

francisduvivier wrote: post #60

Some people here were asking for it so I quickly vibe forked a speed control slider for farming some karma here on Hacker News: https://francisduvivier.github.io/eternal-struggle-with-spee... Code: https://github.com/francisduvivier/eternal-struggle-with-spe...

[deleted]

Re: Eternal Struggle

#96

Post by maxlin »

francisduvivier wrote: post #60

Some people here were asking for it so I quickly vibe forked a speed control slider for farming some karma here on Hacker News: https://francisduvivier.github.io/eternal-struggle-with-spee... Code: https://github.com/francisduvivier/eternal-struggle-with-spe...

Thanks :D I did really want to know what kind of shape it would tend towards over time.

Running 100x for some moments, the white part got pincer maneuvered by the black and I ended up with the whole circle becoming black. Don't know what to think of that lol

Re: Eternal Struggle

#98

Post by aoeusnth1 »

SonOfLilit wrote: post #28
MrJohz wrote: post #11

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.

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.

Re: Eternal Struggle

#99

Post by narrator »

francisduvivier wrote: post #60

Some people here were asking for it so I quickly vibe forked a speed control slider for farming some karma here on Hacker News: https://francisduvivier.github.io/eternal-struggle-with-spee... Code: https://github.com/francisduvivier/eternal-struggle-with-spe...

It looks like it converges to a normal distribution curve with white being the area under the curve.
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