Luke DuBois introduced us to Paul Bourke, a researcher from Australia who shares an amazing online repository of math equations for geometry, textures, shapes and fractals. I tinkered with some of these equations through a JavaScript file in Max/MSP/Jitter.
I created the shapes using little cubes at each point, one point at a time. You can watch the shape take form:
I settled on the Klein Bottle shape. Here’s a patch that forms the shape with a fun visualization and sonifies it, allowing you to tinker with parameters like # of points and size of the cube at each point.