This is an animated gif of a quasicrystal:

(it's 2MB, give it a minute to load...)

Done in processing. Original inspiration: https://web.archive.org/web/20150728060946/http://spacecollective.org/michaelerule/5810/Quasicrystal-Diffraction-Patterns (found on the EMSL linkblog). The math is really easy: just 5 1-D sinusoids in equally-spaced directions. Add them up, map them to hue, a little phase change, and presto. An interactive version forthcoming: change the frequency, number, and directions, and maybe color map....