Tiling

We are indebted to Escher, an artist, for popularizing this mathematical topic. The idea is to find shapes that have the property that, given and endless supply of exact replicas, we could use them to completely cover the plane. Escher studied methods to develop such shapes methodically.

A good friend and artist/sculptor, Patricia Uchill Simons, encouraged me to enter a submission for an Escher Symmetry show. The catch was that, if selected, you had to implement the tiling in clay tiles (This was sponsored by a professional ceramics society). Pat promised to help if my design was selected. At a department meeting, I sketched out the fundamental design for my submission. I then used software (Corel Draw) to implement the plan with precision. It looked like a dog to me, so I dubbed it the Joshua Tile after my Irish Setter, Joshua.

My design was selected as one of the twelve chosen from among more than 70 submissions. I was later told that it was chosen not so much for the artistic merit but because of the precision. My tiles fit together so well that I did not need to use grout to fill in between tiles.

The fundamental tile:

was developed using basic Escher rules for slides and glide rotations from an equilateral triangle. It was colorized and marked for etching:

Then I tiled with it. Six fit together thusly:

A cookie cutter was developed for the final cutting of the tiles. Then Pat Uchill Simons gave generously of her time, her studio, and her kiln. With her guidance the pieces were cut and fired.

A second friend and artist, James Barfoot, saw a loose assemblage of the pieces. They formed hexagons that would fit together. He encouraged me to think more creatively, to make it more dynamic. The end result was a more Escher-esque piece.

Framed, it was sent out to be part of the Symmetry show in the Science Museum in San Diego. I completed the display by showing one complete hexagonal grouping, one hexagonal grouping almost complete, except for the tiles flying in from the right, and one grouping with tromp d'oeuil. In this last grouping, two tiles are missing entirely. One of the missing tiles still provides the shape by its absence, however. The final tile is incomplete, yet your eye wants to finish it.