Taming the wire
Scharein's KnotPlot forces, as van Wijk and Cohen use them: each point of the wire is pulled by its two neighbours (F_a = H\,r^{1+\beta}) and pushed by every other point (F_r = K\,r^{-(2+\alpha)}), damped, and a move that would take a strand through another is refused, so the knot type cannot change. What is tamed is a fat knot, a solid torus that is never shown and has no film: the forces act across the gaps between its surfaces, so wherever two strands pass they are a tube's diameter apart and more. The wire, a thin knot inside it, follows its core, and the film follows the wire. The knot grows while it relaxes.