Tesselations
I’ve posted several links to tessellations before (and if you can’t find them here via the search box it’s probably because I misspelled it tesselation in the past), but I don’t think I ever saw animated ones: Take a look at Tesselating Animation – it has 23 animated tessellations. I found the link on this MetaFilter thread, which in turn linked to an older thread about an animation of a drawing by M. C. Escher. The original drawing has a blank space in the middle, and Hendrik Lenstra calculated what belongs there (New York Times link).
(And for reference, I’ve added this link to my collection of Escher links.)