Abstract

We study the problem of partitioning a disc into N connected regions with two different areas while minimizing the perimeter. This becomes progressively more challenging as N increases due to the combinatorial increase in possible configurations. To address this issue, we propose an approach based on minima of a system of particles interacting via a potential function. These act as seed points for a Voronoi diagram, which gives appropriate topologies for the minimum perimeter, which are then evaluated using the Surface Evolver software. Our preliminary results indicate that this method accurately reproduces all existing conjectured candidates for N ≤ 10, while reducing computational resources. Moreover, we extend our findings by predicting potential candidate solutions for the least perimeter partition of a disc for N > 10.