# Karl Kattchee

Associate Professor of Mathematics

University of Wisconsin-La Crosse

Mathematics can be the subject of art, or it can be part of the process. Sometimes both happen at the same time. I like to experiment, and I have used pencil, pen, pastel, acrylic, paper, cardboard, scanners, cameras, computers, printers, metals, and wood in creating mathematical artwork. This year, my work is based upon de Bruijn sequences of order four, which are binary strings of length 16 whose contiguous length-four substrings form the collection of all possible length-four binary strings.

De Bruijn Music #2

18 x 31 cm

digital print

2018

This is an array of mathematical and visual information. Each row is a representative of one of the four natural equivalence classes of order-four de Bruijn sequences (circle=0 and dot=1). Each de Bruijn sequence can be replaced with a permutation of the numbers 0,1,2,...,15 by converting each length-four substring into its decimal form as a number. The coloring scheme is based on these permutations.