Soap film
Realizes: minimal surface (Plateau's problem)
A soap film spanning a closed wire boundary settles into the surface of minimum area — the solution to Plateau's problem. For two parallel rings it realizes a catenoid. Can approximate Steiner trees for planar point sets. Speed: seconds to minutes (surface tension equilibration). Capacity: continuous optimization over infinite-dimensional space.
Examples
Soap Film Minimal Surface Demonstration
Physical demonstration of soap films forming minimal surfaces and solving Plateau's problem with wire frame boundaries
Soap Film Steiner Tree Solution
Demonstration of soap films automatically finding shortest connecting paths between points, approximating Steiner tree solutions
Soap Films and Minimal Surfaces
Educational video showing how soap films solve complex minimal surface problems that are difficult to calculate mathematically