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# Math as Muse

Photonics Spectra
Apr 2008
Michael A. Greenwood

The inspiration of Dutch artist M.C. Escher lives on.

The famous graphic artist was known for creating mesmerizing images that drew viewers in with their near-symmetrical perfection.

A new generation of math-inspired artists is following in the master’s footsteps, finding its muse in the complex patterns that are generated by formulas, equations and symmetry. More than 40 such artists recently showed their creations at an exhibit in San Diego.

Figure 1. “Coral Star.” Courtesy of Michael Field.

One of them, Michael Field, a mathematics professor at the University of Houston in Texas, takes inspiration from dynamical systems, which determine how a point moves around a plane. Field uses a symmetric equation that takes any point on a piece of paper and moves the point to a different spot, repeating this process again and again — up to several billion times.

After keeping track of how often each pixel-size spot is landed on, he colors the spots according to the number of times they are visited. Even though the equation describes “chaotic” dynamics, the resulting colored image often has very fine detail and structure.

Figure 2. Fathauer crystal. Courtesy of Robert Fathauer, Hank Kaczmarski and Nicholas Duchnowski.

The resulting symmetry can be quite startling. In “Coral Star” (Figure 1), the image becomes more intricate as it gets closer and closer to the center. A black background further highlights the nuances and shades of the design.

Another artist, Robert Fathauer of Phoenix, was looking for a way to arrange squares in a repeating pattern. He started with a red cube and placed five half-size orange cubes on its exposed face (Figure 2). Next, he added five smaller yellow cubes onto the faces of each of these, and then five smaller greenish cubes on the faces of those, and so on and on.

colored imageCoral StarLighter Sidesymmetry