# Karl Kattchee

“By using mathematics as part of the creative process, I can infuse my art with mathematics without necessarily representing any particular mathematical thing. On the other hand, the mathematical content may be right at the surface. Mathematical art can be conceptual, too. I use pencil, pen, pastel, paper, cardboard, scanner, camera, computer, printer, and metals to achieve my desired effects.”

This image is a classification of all closed paths, on a 6x6 grid, with the following properties: First, each path must proceed around the center of the grid and be orthogonal in the sense that every turn is 90 degrees. Also, the path must use each row and column exactly once. Finally, we require that each path be asymmetrical, and we do not distinguish between paths which differ by a rotation or flip. Each center square is colored black, and the shades of red are dictated by the winding number of each region.

Acknowledgements: Craig Kaplan (Waterloo), for helpful notation and the coloring scheme idea, and artists Kate Hawkes and Misha Bolstad (UW-La Crosse) for the poppies idea.

The outcome of a roll of the DA DA dice is a discrete random variable X with a singleton sample space (DADA). The probability of DADA is P(DADA)=1, so the expected value of X is E(X)=DADA.

Acknowledgement: Brad Nichols (UW-La Crosse), for assistance with metalsmithing.