butterfly curve

Temple Fay discovered this complicated curve in 1989. It can be defined either parametrically or as a polar equation; I did it the former way.

One application I thought of for this is object motion in games: I tried it out by writing this little Canvas game, where the comets follow the curve's trajectory. The differences in plot density along the curve create natural-looking comet tails.

bézier curves

De Casteljau's algorithm is a fast, numerically stable way to rasterize Bézier curves. This code implements an interactive demo: click to append nodes to the curve's defining polygon, and drag any node to alter the curve.