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.
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.