English mathematician Sir Roger Penrose has written about relativity, cosmology, aritificial intelligence, and the nature of human consciousness (an anti-programmer debating society named itself after him). If one is not prepared to consider the merits of Penrose’s controversial arguments about the relation of Gödel’s incompleteness theorem or quantum phenomena like microtubules to the task of creating artifician intelligence, you can appreciate the creation that Penrose is perhaps best known for: Penrose tiling. Tessellation — tiling the plane so as not to leave any gaps — has long been of interest to artists, from the artists who created the Alhambra to M.C. Escher. Tessellations come in all shapes and sizes. When Martin Gardner published a list of eight convex pentagon tessellations, thought to be a complete list, a reader discovered a ninth type; Marjorie Rice, a San Diego housewife and mathematical layperson, then devised a method for investigating and found three more. (Fourteen regular tesselations using convex pentagons are now known, but this list has not been proved to be complete.) Escher’s tessellations are world famous, available on everything from posters to outdoor tiles (thanks, Kathryn!). But Penrose had worked out (by hand) a quasitessellation, a system by which two shapes could be used to tile the plane without ever repeating the pattern. This aperioditc pattern, based on "kites" and "darts" could be used to make anything from decorative floors to intricate, jigsaw-like puzzles. Penrose’s interest in tessellation perhaps triggered some happy memories; a teenaged Roger and his father had invented Escher’s impossible shapes, the tribar and the Escher cube. And it’s given rise to another distinction: Sir Roger is almost assuredly the only one of Stephen Hawking’s collaborators ever to file a lawsuit over toilet paper copyright.