Swenson College of Science & Engineering: Faculty Directory

Featured Faculty: Doug Dunham

Professor, Department of Computer Science

Interests: Computer generated repeating patterns, the mathematics of M.C. Escher's art, pattern generation algorithms in hyperbolic geometry

Courses Taught: CS 4511 (Computability and Complexity), CS 4521 (Algorithms and Data Structures), CS 5551 (User Interface Design), CS 5721 (Computer Graphics)

Website: http://www.d.umn.edu/~ddunham/

Dr. Dunham's research has focused on using computer graphics methods to create repeating patterns of the hyperbolic plane. This work was inspired by the four "Circle Limit" patterns of the Dutch graphic artist M.C. Escher, which he created by hand about 50 years ago. About 20 years later, Dr. Dunham and his students reconstructed those patterns via computer graphics. Since that time, Dr. Dunham, with the help of other students, has added to the capabilities of the first program, allowing for the creation of new patterns such as the one shown below.

A six-colored hyperbolic fish pattern

The pattern above was featured on the poster for Math Awareness Month 2003. One can interpret this design as a repeating pattern in the Poincaré circle model of hyperbolic geometry. The fish are colored symmetrically: all fish along a backbone line are the same color, and they adhere to the map-coloring principle that adjacent fish should be different colors. There is more information about this pattern in the essay Hyperbolic Art and the Poster Pattern.

Dr. Dunham's teaching interests in computer graphics and computer science theory complement his research interests. He has involved 30 graduate students and more than 30 UROP students in his research projects. He has also won the Jean G. Blehart Distinguished Teaching Award.