Python code for the animation of a cubic dipole cluster (Version 1.2)

A cubic dipole cluster has a degenerate ground state with a continuum of solutions, which can be experimentally realized with spherical magnets [1]. With this animation, one can step through the one-parameter family of ground state solutions, and watch the ensuing field in a number of projections.

These cubic dipole clusters are reminiscent of dotriacontapoles, in the sense that their field falls off with the  7^th power, and their interaction force falls off with the remarkable 12^th power. The second part of the animation shows that this law is independent of the ground state orientation. The prefactor changes, however, and might even change sign.

[1] “Assembly of eight spherical magnets into a dotriacontapole configuration” by Stefan Hartung, Felix Sommer, Simeon Völkel, Johannes Schönke, and Ingo Rehberg, Phys. Rev. B 98, 214424,  and Refs. cited therein.