The Thomson problem investigates how identical electric charges arrange themselves on the surface of a sphere to minimize their total electrostatic potential energy. As the number of charges increases, finding the lowest-energy configuration becomes increasingly challenging because of the many possible local minima.
This Mathematica simulation explores three optimization approaches: random initialization, removing a charge from an optimized configuration of (N+1) charges, and adding a charge to a configuration of (N-1) charges. By comparing the resulting energies and three-dimensional arrangements, the simulation investigates how neighboring configurations can be used to efficiently identify low-energy structures.
