Are large two-dimensional clusters of perimeter-minimizing bubbles of equal-area hexagonal or circular?

TL;DR

This study uses computer simulations to demonstrate that rounding large, equal-area bubble clusters can reduce their perimeter, supporting the idea that perimeter-minimizing clusters tend to be more circular or hexagonal.

Contribution

First computational evidence showing that rounding improves perimeter minimization in large, equal-area bubble clusters.

Findings

Rounding reduces perimeter in large bubble clusters

Hexagonal and circular shapes are optimal for perimeter minimization

Clusters of up to 200,000 bubbles analyzed

Abstract

A computer study of clusters of up to 200,000 equal-area bubbles shows for the first time that rounding conjectured optimal hexagonal planar soap bubble clusters reduces perimeter.