Idea: music visualization with spring networks

The basic idea is to connect a collection of springs into an arbitrary graph, then drive certain points in this graph with the waveform of a piece of music (possibly with some filtering, band separation, etc.) This could be restrained to two dimensions or allowed unrestricted use of three.

Spring constants could be chosen so the springs resonate with tones in the key of the piece. Choosing these constants and the graph connectivity to be aesthetically pleasing would likely be an art form in of itself. A good starting point would be interconnected concentric polygonal rings of varying stiffness. Symmetry seems like a must.

For a software implementation, a useful starting point would be CS 176 project 5; a cloth simulator that considers only edge terms is essentially a spring-network simulator. There are many ways to render the output; for example, draw nodes with opacity proportional to velocity, and/or draw edges with opacity proportional to stored energy. Use saturated colors on a black background, and render on top of blurred previous frames for a nice trail effect. Since I've already coded the gnarly math once, I might try to throw this together tomorrow evening, if I don't get distracted by something else.

The variations are really endless. For example, with gravity and stiff (or entirely rigid) edges, you could make a chaos pendulum. By allowing edges to dynamically break and form based on proximity and/or energy, you could get all kinds of dynamic clustering behavior, which might look like molecules forming or something.

A hardware implementation (i.e., actual springs) would be badass in the extreme, although I imagine it would be finicky to set up and tune.