Kevin Lee using designs by Alain Nicolas and M. C. Escher.
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.
Lately, I have been exploring techniques to laser cut and engrave tiles out of wood. Different species of wood are used to create contrasting tiles that are inlaid to decorate boxes and chessboards. The tessellations featured on the box were created in TesselManiac! by the incredibly talented artist, Alain Nicolas.
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.
The great French tessellation artist, Alain Nicolas, has been testing my new tessellation program. Several times a week for the last six months he has delighted me with amazing tessellations that he has created using TesselManiac! The faces of this inlaid wood box showcase seven of his new designs. The front of the box uses a clever Cat and Mouse motif that is of Heesch type TCTGG. The morph algorithm in TesselManiac has been used to generate tiles that show how the initial polygon morphs to the finished motif. The top uses two cowboy designs by Nicolas that are both of extended Heesch type G’G’G’G’ (Heesch type G1G1G2G2 with an added interior reflection line). The remaining sides illustrate Heesch types TCCTCC, TG1G1TG2G2, and TGTG.