Universal Optimal Configurations for the p-frame Potentials
This page is associated with the paper “Universal Optimal Configurations for the p-Frame Potentials” by Chen, Gonzalez, Goodman, Kang, and Okoudjou. It contains code used to check the (now solved) conjecture that LkN frames minimize various p-frame potentials. The program improves randomly chosen frames using a basic gradient descent procedure and compares these to the LkN potential. We use this program only as a guide; some improvements can likely be made. This code was written in connection with the University of Maryland MAPS-REU, funded by the NSF.
Python code is available here. The program uses some features of SageMath to run. Results from the code may be found below for the various cases.
One frame was found with a lower frame potential (see L44 test #27), but the difference seems within the realm of numerical error (-4.4408920985e-16).