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Deltanic

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I found that these rings get exponentially smaller, approximately generating around a radius of sqrt(x / 2) * 2^15. That would mean that up until the world border of 30,000,000 blocks, there are at least well over 6500 rings, or over 3250 void gaps. That's not counting partial rings in the world's corners. If it's of any help, I documented my findings here, along with a list of coordinates of the first 10 rings for those interested:

https://gist.github.com/Deltanic/b98d005c9025f10a67de9e966fa57ebb