I ran into this problem working on differential equations that model pattern formation (reaction-diffusion equations, originally postulated by Turing in the 1950s). The equations are highly nonlinear, but some solutions can be found when solving the problem on a sphere. You get spot solutions that dynamically move essentially to the minimum energy configuration (Fekete points I believe are called). BTW, Neil Sloane, of OEIS fame, has a list of the best packings, up to n=100 I believe [0].
Things get interesting when you also allow the sphere to grow, the spots start to split (and sometimes annihilate), understanding how the spots move on the sphere is itself a very interesting problem.
Things get interesting when you also allow the sphere to grow, the spots start to split (and sometimes annihilate), understanding how the spots move on the sphere is itself a very interesting problem.
[0] http://neilsloane.com/packings/