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Symmetry and Perspective

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UMD Professor Creates Digital Art

Doug Dunham
Doug Dunham and "Butterflies," art using repeating patterns related to hyperbolic geometry. This piece is located in the Computer Science Office, 320 Heller Hall.  
Doug Dunham uses computer science to merge mathematics and artistic expression.  

Mathematics and the graphic arts have had an important relationship for centuries. The concepts of symmetry and perspective are seen in the art of ancient Mexico, China, Peru, Egypt, and other areas.

In recent years, the advent of computers allowed the development of various forms of digital art, giving artists and mathematicians a new platform for expression.

UMD Professor Doug Dunham, Department of Computer Science, has been inspired to create his own unique brand of mathematical art, and has been accepted in the Mathematical Art Exhibition at the Bridges Conference and Joint Mathematics Meeting nearly every year since 2010.

“The patterns are inspired by those of M.C. Escher, and like Escher's patterns, they have no gaps or overlaps,” Dunham said. Dunham has been interested in Escher since the 1970s and in 2013 organized a trip to the Escher Museum in The Hague, Netherlands, for computer scientists and mathematicians.

The goal of his art is to create aesthetically pleasing repeating patterns related to hyperbolic geometry. Dunham is one of only 10 or so computer scientists/mathematicians in the world to create artistic images of this kind. The Mathematical Art Exhibition accepts work from many researchers each year. They enter pieces such as molecular structures fashioned from beads or the mathematical polyhedra created from wood.

Dunham uses the process as a teaching tool for UMD undergraduate and graduate students in the computer science program. In the past three decades, teams led by Dunham’s vision have written computer programs for about 30 patterns. They create images of interlocking fish, bats, lizards, butterflies, angels, devils, and other creatures. Students get real-world experience. They learn skills and techniques that apply to computer software design in various industries, and they learn the mathematics behind a computer code.

“The complexity of the art has increased as computers became more sophisticated,” Dunham said. At first the images were simpler and one- or two-dimensional but have grown into three-dimensional objects of increasing intricacy.  Even the printing technology has changed the output. Before color printers, Dunham used to color the images by hand.

“This work shows that mathematical objects can be beautiful,” Dunham said.

Examples of Doug Dunham's Mathematical Art

2010 2011 2012 2013  

Those Who Can, Duluth

Story by Cheryl Reitan. January, 2014.

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