JMM 2005 Exhibit - Anne Burns

Anne Burns

"Iterated Mobius Transformations"

Digital print, 2004

"Mathscape"

Digital print, 2003

Anne Burns began her studies as an art major. Years later she took a course in College Algebra, loved it, and just kept going until she received a Ph.D. in Mathematics from SUNY at Stony Brook. She is now a professor of Mathematics at LIU. Her research and publications are in the areas of Dynamical Systems and Computer Graphics. She spends her free time combining her love of nature, mathematics and art.

"I am a very visual person; before I became a mathematician I was a painter. When I prove something in mathematics I must first convince myself of its truth with a visual argument. Computers make it possible to "see" the beauty of mathematics. I love the logic of programming and using the computer to translate functions and relations into aesthetically pleasing patterns and pictures.

"The title of the piece, Iterated Mobius Transformations, pretty much describes the mathematics used. I started with an array of 13 Möbius Transformations; 12 of them map the unit circle into a chain of pairwise tangent circles which are also tangent to the unit circle, and the 13th maps the unit circle to a small circle centered at the origin tangent to the other 12. Each of these transformations is composed with a transformation from the Unit Circle Group, SU(1,1), resulting in an array of 13 transformations which form an Iterated Function System. This picture shows the fourth iteration.

"Mathscape, was created using a variety of mathematical formulas. The clouds and plant life are generated using fractal methods. The mountains are created using trigonometric sums with randomly generated coefficients; then, using 3-D transformations, they are projected onto the computer screen. Value and color are functions of the dot product of the normal to the surface with a specified light vector.

"More of my art including many "mathscapes", circle pictures, interactive art and animations can be found on my website, http://myweb.cwpost.liu.edu/aburns/. You can e-mail me at aburns@liu.edu."