Foamy Partition, Weaire-Phelan

My print "Foamy Partition: Weaire-Phelan" gives an interior view of a soap froth. Mathematically, a foam or froth is usually considered as an infinite collection of touching soap bubbles, each trying to minimize its area while fixing the volume of air enclosed. In the 1880s, Lord Kelvin considered the problem of finding the optimal equal-volume foam, partitioning space into unit-volume cells. His conjectured solution (using bubbles all of the same shape) stood for over 100 years, until in 1994 the Irish foam physicists Weaire and Phelan discovered this more complicated but also more efficient structure. Some of its bubbles are pentagonal dodecahedra, but others have fourteen faces.

Optiverse, Framework Interior

From from the 1998 sphere-eversion video "The Optiverse", which was a joint project with George Francis, Stuart Levy, and Camille Goudeseune. A sphere eversion is a mathematical process of turning a sphere inside-out. To physically turn a sphere inside-out, one would have to cut a hole in the surface, then turn the rest inside-out like a sock, and finally patch the hole. To make an interesting mathematical problem, we do not allow the hole; however to make the eversion possible, we must allow the surface to pass through itself. In an eversion, the spherical surface remains everywhere smooth and connected, but two different parts may cut through one another without even noticing.

Optiverse, Minimax Sphere Eversion

Minimax Sphere Eversion shows a triangulated computer simulation of part of the everting sphere; the open framework makes the computational grid clear, while the white tubes show the self-intersections of the surface. "Optiverse: Minimax Sphere Eversion" uses bubble-like transparency; the whole eversion is shown in small images around the border, while the large central image highlights one of the most complicated middle stages.