I am looking for the name of the algorithm that fills space with equally-distant cells. If n = 2, the space is split in half. If N = 3 it is split into three cells. I think it would require kangaroo for each additional cell to settle into to equilibrium. It is similar to voranoi, but the centers of the cells adjust so all points are equally spaced.

In 2d you can’t have more than 3 points where each is equidistant from all the other points, and in 3d no more than 4.

Maybe you mean just equidistant from some set of neighbours? In which case look for circle packing.

Yes, something like sphere packing, but the size of the spheres adapts to the number of spheres so it completely fills the space.