[swesnow]

1: Sorry about that, the default 20,000 is to make it look nice on computers but I should probably drop it a bit for phones, that's reasonable. 2: Yeah this part is important and cool and not entirely obvious until you solve the differential equation. I did a 3D simulation of a somewhat related situation (Thompson problem) once. But it would be very interesting to figure out if there is a 3D potential function that gives uniform density in the same way as the Ginibri (Q(z) = |z|^2) potential. Good idea for future work :) 3: Make sure you try the lemniscate potentials as well which are not rotationally symmetric. I want to try adding even more potentials in the future but these two families are those which has been subject to the most research.

Thanks for playing around with the tool!

[gus_massa]

I got better results with N=100, and the time and frames bars at the top in the middle. It reach the equilibrium in ~5 seconds, so it's easy to test and compare the different potentials. #ResearchInTheTikTokEra :)

With z^20, the problem is that when you change the number of particles, the ones are distributed randomly and the ones near the corners have a huge gradient and probably overflow and the inifinites/nans are viral and kill all the other particles. The trick is to switch to z^2, change N wait a moment and then change to z^20. Perhaps you can clip some values or try some trick like in stiff equations.

In 3D, I expected a z^2 potencial with a 1/z^2 force to generate an uniform distribution, for something something Gauss. (It's just bad hand-waving, I didn't have anything close to a proof.) It's interesting that it is so easy.