Karl Kattchee and Craig Kaplan

Associate Professor of Mathematics and Associate Professor of Computer Science
Mathematics and Statistics Department, University of Wisconsin-La Crosse and Cheriton School of Computer Science, University of Waterloo
La Crosse, WI and Waterloo, Canada

We share a fascination with doodles that follow different kinds of rules and constraints. Mathematically, we are interested in classifying and counting them. Artistically, we are interested in presenting them in an impactful way.

10512 Poppies
10512 Poppies
28 x 21 x 2 cm
ink on paper

This piece is a classification of all closed paths, on an 8x8 grid, with the following properties: (1) The path must proceed around the center of the grid and be orthogonal in the sense that every turn is 90 degrees, and (2) The path must use each row and column exactly once.

It turns out that there are 10512 such "poppies" (including 288 symmetric ones). They are all printed out on 110 sheets of paper. We use a coloring scheme based on winding number, and each poppy is accompanied by Kaplan's useful combinatorial notation.