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.
| N | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Output (text files) |
L13 L23 L33 |
L14 L24 L34 L44 |
L15 L25 L35 L45 L55 |
L16 L26 L36 L46 L56 L66 |
L17 L27 L37 L47 L57 L67 L77 |
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).