This minimal surface is a cross between acatenoid andhelicoid. It would be interesting to see what really happens when a spring is covered with a soap film. Click here to download some POV-Ray code. Here is some Mathematica code:
(* runtime: 0.6 second *)
x := Sin[alpha]Cosh[v]; y := Cos[alpha]Sinh[v];
Do[ParametricPlot3D[{x Cos[u] + y Sin[u], x Sin[u] - y Cos[u], u Cos[alpha] + v Sin[alpha]}, {u, 0, 2Pi}, {v, -2.25, 2.25}, PlotPoints -> {36, 10}], {alpha, -Pi/2, Pi/2, Pi/18}];

Links

• Venice Museum Bridge – bridge proposal, by Eric Worcester
• Marina Bayfront Pedestrian Bridge – double-helix bridge in Singapore
• Soap Film Coil Photo – by the Exploratorium