AllRGB sets an unusual challenge: create a 4096×4096 image such that every possible RGB value is present once and only once. Most of the images look like the gray soup you'd imagine, but a few actually depict a real scene surprisingly well, and some are interesting as abstract art:
Eric Burnett wrote about his allRGB Mandelbrot, which uses Hilbert curve techniques, as does Aldo Cortesi's portrait of the Hilbert curve. Conflict of interest disclosure: the gray background on my blog is a Hilbert curve. ☺
Of course, there's no practical purpose to these techniques, but they're interesting explorations of color spaces and image rendering.