Alternatively for the non-random and arbitrary N case here, an approach based on Phyllotaxis that samples a Fermat spiral every ~137.508 degrees (i.e., the golden angle, or the golden ratio fraction of a circle) also works pretty well: https://en.wikipedia.org/wiki/Fermat%27s_spiral#The_golden_r.... It works nicely for any N, even if the N isn't square or close to square (just choose the scaling appropriately, e.g., c = 1/sqrt(N)).
A copy of the original paper can be found here and is nice and easy to read, with pseudocode: https://web.archive.org/web/20190223095317id_/http://pdfs.se...
Alternatively for the non-random and arbitrary N case here, an approach based on Phyllotaxis that samples a Fermat spiral every ~137.508 degrees (i.e., the golden angle, or the golden ratio fraction of a circle) also works pretty well: https://en.wikipedia.org/wiki/Fermat%27s_spiral#The_golden_r.... It works nicely for any N, even if the N isn't square or close to square (just choose the scaling appropriately, e.g., c = 1/sqrt(N)).