CHAPTER 13 - Soap Bubble Clusters

Abstract

Soap bubble clusters illustrate simple mathematical principles. Despite notable progress, they defy complete mathematical explanation. A single soap bubble quickly finds the least-surface-area way to enclose the fixed volume of air trapped inside—the round sphere. Similarly, bubble clusters seek the least-area way to enclose and separate several regions of prescribed volumes. This principle of area minimization alone, implemented on Ken Brakke's Surface Evolver, yields computer simulations of bubble clusters, from the video Computing Soap Films and Crystals by the Minimal Surface Team at the Geometry Center (formerly the Minnesota Geometry Supercomputer Project). Soap bubble clusters do not always find the absolute least-area shape. The chapter illustrates two clusters enclosing and separating the same five volumes. In the first, the tiny fifth volume is comfortably nestled deep in the crevice between the largest bubbles. In the second, the tiny fifth volume less comfortably sits between the medium-size bubbles. The first cluster has less surface area than the second. It might be still better to put the smallest bubble around in back.