Filaments and voids in planar central configurations

TL;DR

This paper numerically investigates planar central configurations of 1000 equal-mass bodies, revealing filamentary and void structures related to the complexity measure, and proposes a classification based on this complexity.

Contribution

It introduces a novel classification of central configurations based on a complexity measure and uncovers filament and void patterns in large-scale configurations.

Findings

Filaments and voids are present in configurations with varying complexity.

A new classification scheme for central configurations is proposed.

Numerical methods successfully analyzed large-scale configurations.

Abstract

We have numerically computed planar central configurations of $n=1000$ bodies of equal masses. A classification of central configurations is proposed based on the numerical value of the complexity, $\mathcal{C}$. The main result of our work is the discovery of filaments and voids in planar central configurations with random complexity values. Suggestions are given for future work in the context of central configurations with random complexity values.