Thomson Problem Solutions

number of points

20

plot type

2D

3D

In the Thomson problem,

n

point charges are placed on the surface of a unit sphere in such a way as to minimize the total energy of the system. These solutions place each point so that its nearest neighbors are as far away as possible.

This Demonstration uses precalculated data from[1], which represents many years of research and optimization. Officially, the problem is only solved for 1 to 6 and 12 points; all other solutions are considered "best known." For code that solves the Thomson problem, see the Related Links.

References

[1] D. J. Wales and S. Ulker. "Global Minima for the Thomson Problem." (Jan 4, 2016) www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html.

[2] Wikipedia. "Thomson Problem," (Jan 4, 2016) en.wikipedia.org/wiki/Thomson_problem.

External Links

Optimizing Diffusion-Weighted MRI Using Electrostatic Repulsion

Repulsionhedra and the Thomson Problem

The Thomson Problem with Central Forces

Visualizing the Thomson Problem

Permanent Citation

Ed Pegg Jr

"Thomson Problem Solutions"
http://demonstrations.wolfram.com/ThomsonProblemSolutions/
Wolfram Demonstrations Project
Published: January 5, 2016