Mathematicians, Including Undergraduates, Look at Soap Bubbles

Similarly bubble clusters try to minimize the total surface area enclosing and separating several volumes. Whether the number of enclosed volumes is one or one thousand, it is the same principle of area minimization at work. See FIGURES 2, 3. This principle alone has sufficed to produce computer simulations of bubble clusters, as in the frame in FIGURE 4 from the video "Computing soap films and crystals" by the Minimal Surface Team at the Geometry Center (formerly the Minnesota Geometry Supercomputer Project). Do soap bubble clusters always find the absolute least-area shape? Not always: FIGURE 5 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, although I do not know' for sure that there is not a third possibility of still less area.