Feb 28, 2008

Math on Display

Visualizations of mathematics create remarkable artwork

Source: Science News
Written by Julie J. Rehmeyer

“Coral Star” shows the motion brought about by one particular dynamical system.
By Michael Field

Mathematicians often rhapsodize about the austere elegance of a well-wrought proof. But math also has a simpler sort of beauty that is perhaps easier to appreciate: It can be used to create objects that are just plain pretty—and fascinating to boot.

That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meetings in San Diego in January, where more than 40 artists showed their creations.

Michael Field, a mathematics professor at the University of Houston, finds artistic inspiration in his work on dynamical systems. A mathematical dynamical system is just any rule that determines how a point moves around a plane. Field uses an equation that takes any point on a piece of paper and moves it to a different spot. Field repeats this process over and over again—around 5 billion times—and keeps track of how often each pixel-sized spot in the plane gets landed on. The more often a pixel gets hit, the deeper the shade Field colors it.

The reason mathematicians are so fascinated by dynamical systems is that very simple equations can produce very complicated behavior. Field has found that such complex behavior can create some beautiful images. For example, the dynamical system he depicts in “Coral Star” does some peculiar things as it gets closer to the center (technically, the equation is discontinuous at the origin). So as you get closer and closer to the center, the image gets more and more complex.

“Even apart from the center, the image has quite a lot of depth to it,” Field says. “It’s a feature of the way it’s colored. I’m not so keen on bright primary colors. The shading makes it more interesting.”

This image has an unusual 35-fold symmetry, and Field created it as a present for his wife on their 35th anniversary.

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The website for the exhibition is at

Copies of the catalogue for the exhibit, complete with high-quality reproductions of all the pieces of art, are for sale at

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