This Java applet was compiled under Java 1.1.7 which was released in November of 1998. If your browser gives you errors while trying to run this applet, it is likely because it does not have the most recent Java version. In fact, you are likely to have Java 1.0 in that case, which is pretty darned old, so you should update.

The point of this applet is to find the equilibrium configurations of repulsive points on the surface of a sphere. These equilibrium configurations are not unique, so it is possible to find more than one configuration for a given number of points, however, some equilibria are more stable than others, and the most stable equilibria are interesting for various reasons.

Try cases with 2, 3, 4, 6, and 12 points. You might recognize the configurations. If you are patient, you might try 20 points.

The "step" buttons incrementally advance the positions of the points. In many cases, this will get the points in an equilibrium position. Be careful, though, since pressing with a large number of points, the procedure can take a very long time. For now, the advancing routine does not work well for more than about 12 points, but this might improve if I waste more time on this.

The "boost" parameter is tricky to use but can speed up the search for equilibria if you use it correctly. If you use a large boost too much, what you will find is that your system oscillates wildly, so use "boost" sparingly.

The "distance from equilibrium" tells how far the system is from being in a equilibrium state. When that parameter is zero, the state is in equilibrium. In practice, that parameter rarely gets smaller than 1.0e-16 due to machine precision. A value near 1.0e-6 means that the system is pretty close to equilibrium, to the extent that the points do not appear to move around. Values greater than or near 1.0e-4 are not very near an equilibrium.

The "print" button which will list the position of the points in the text area with the scroll bars.

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The three views here are from the top, and from two sides, of the set of points. The red and green points are intended to be references points to orient your perception of these projections. When the points are farther away, they are drawn smaller. When the points are closer, they are drawn larger.