Kevin Lee using designs by M. C. Escher, Alain Nicolas, and Jos Leys

Statement

For several years I have written software to create Escher-like tessellations. The goal of my new program, TesselManiac!, is to have users (especially young ones) create tessellations and explore this connection of math and art. TesselManiac! allows you to create thirty-three types of isohedral tessellations. It includes several animations, including one where the tile morphs from a base polygon tile to the final shape. During my sabbatical last year Craig Kaplan at the University of Waterloo helped me improve the tile-morphing algorithms. In my inlaid tessellated chessboards displayed here, the usual square tiles morph to various shapes, but the points where four tiles meet are exactly the vertices of the square grid of a chessboard.

Artworks

Alain Nicolas created an elegant C4C4C4C4 bird tile. Sixty-four tiles and four border pieces were laser-engraved and cut to create one side of this chessboard. If you define the center four tiles as ring one, then rings two and three are filled with complete bird tiles and rings one and four are composed of partially-formed tiles. The partial tiles follow the rule that all tile edges are straight unless the edge is shared with a full tile from ring two or three. Nicolas’s bird tiling also decorates the engraved stand. The second side of this chessboard (image on my website) features a sea turtle tessellation by Jos Leys. This time the full tiles are in rings one and four and the partial tiles are in rings two and three.

Escher's print Development I shows a 10 x 10 checkerboard grid in which the outer ring of square tiles morphs to the center ring of four fully-formed lizards. The lizard tile was taken from his regular division drawing #15 and is of Heesch type C4C4C4C4. In Escher's own classification system, that tile is type IXD. The motif is based on a square and has centers of 4-fold rotations at two corners. Escher places one of these corners at the center of the checkerboard, matching the 4-fold center of the checkerboard that interchanges light and dark squares. I used my software and a laser cutter/engraver to create a traditional 8 x 8 chessboard of wood tiles that morph into Escher’s lizards. Escher’s Lizards © The M.C. Escher Company B.V.