Rubber-band Steiner tree

Elastic bands stretched between pins hammered into a board relax under tension to a state of minimum total length. Because each band pulls with a force proportional to its extension, the equilibrium configuration satisfies the equal-angles condition at every interior junction — the defining property of a Steiner tree. The result is the shortest network connecting all pins, approximating the solution to the NP-hard Euclidean Steiner tree problem. The mechanism is combinatorially distinct from the soap-film Steiner tree (Plateau's problem in 2-D) because the topology of junctions is fixed by the discrete wiring of the bands, not by a continuous surface. Speed: instantaneous (elastic equilibration). Capacity: Steiner tree for ~5-20 pins (limited by physical layout).