Fractal Roots and Artful Math

The term “mathematical art” usually conjures up images of M.C. Escher’s endless staircases, Möbius-strip ants, and mind-boggling tilings. Or it might remind one of the intimate intertwining of mathematics and art during the Renaissance with the development of perspective painting and eye-teasing stagecraft.

A view of the recent MathArt/ArtMath show at the Selby Gallery in Sarasota, Fla. Selby Gallery
Square Roots of a Tree. Courtesy of John Sims
Holly’s Rose: Artwork by Holly Braffet as part of a course offered by John Sims at the Ringling School of Art and Design. Courtesy of John Sims
A digital visualization of pi’s digits. Courtesy of John Sims.

The realm of mathematical art is far wider and more diverse than many people realize, however. A recent exhibition at the Ringling School of Art and Design’s Selby Gallery in Sarasota, Fla., dramatically illustrated the broad range and depth of the burgeoning interaction between mathematics and art.

Titled MathArt/ArtMath, the exhibition was assembled by Kevin Dean, who is director of the Selby Gallery, and John Sims, a mathematician and artist who teaches at the Ringling School. Sims has long encouraged the linking of mathematics and art–in his own work, in the classroom, and by calling attention to the endeavors of others devoted to bringing about such interactions.

“My role as an artist is to encode mathematics in what I do,” Sims remarks. “The mathematical art that I seek to develop combines mathematical language and analysis with the expressiveness and creativity of the process to make expressive visual theorems.”

In constructing his signature piece, Square Roots of a Tree, Sims paired a representation of a tree with a branched fractal structure to highlight the tree-root relationship and interdependency that he sees between mathematics and art. In other orientations, his artwork becomes Tree Root of a Fractal (rotated 180 degrees) and Math Art Brain (rotated 90 degrees).

Tree Root of a Fractal, Sims notes, “shows how the latent geometry of nature can inspire and support abstraction.”

He adds, “To see mathematically, one draws from creativity and intuition, as in the case with the art process itself.”

Sims brings the same sort of sensibility to the classroom. Mathematical ideas inspire artistic creations.

One sequence of artworks arose out of a study of the Pythagorean theorem (given a right triangle with sides a, b, and c, a2 + b2 = c2), particularly the theorem’s manifestations in different guises at different times in history and in different cultures.

It was a journey, Sims says, that blended “the worlds, vocabularies, and strategies of mathematics and art into an interdisciplinary mixture that celebrates the interconnectedness of analysis and creativity, left brain and right brain, theory and practice, structure and expression, and the liberal arts and studio praxis.”

On one occasion, when I visited one of Sims’s art classes, I demonstrated some of the unusual characteristics of Möbius strips and spoke about the diverse ways in which this curious form has been used by artists and graphic designers. The ensuing class assignment had the students making and cutting apart strips to come up with their own interpretations of this intriguing topological object.

Sims has a strong commitment to bringing art–especially mathematical art–to the public. To that end, he promoted the installation of a maze of pillars draped with murals in a Sarasota neighborhood, where visitors could view artworks created by local and internationally known artists and even find space to paint their own artistic impressions.

His most ambitious scheme, TimeSculpture, involves installations scattered across the United States–familiar objects (vase, chess set, chair, clock, and so on) that are connected yet dispersed. Sims sees it as another sort of journey–one that maps “orbits from abstract places into diverse geographies, celebrating the search for cycles in both human and natural systems.”

Sims’s passion for making mathematical art known and accessible to the public led to the MathArt/ArtMath exhibition at the Selby Gallery. The show represented a significant effort not only to illustrate the diversity of mathematical art and but also to illuminate its common threads.

The exhibition presented a broad spectrum of math-related paintings, prints, sculptures, fabrics, digital prints, electronic music, and videos. Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings.

The following artists and mathematicians were represented in the show: Josef Albers, Richard Anuszkiewicz, Tom Banchoff, Jhane Barnes, Max Bill, Mel Bochner, David Cervone, Brent Collins, David Davis, George Deem, Agnes Denes, M.C. Escher, Fred Eversley, Shannon Fagan, Helaman Ferguson, Mike Field, George Francis, Charles Gaines, Paulus Gerdes, Bathsheba Grossman, Al Held, John Hiigli, Slavik Jablan, Alfred Jensen, Adrienne Klein, Sol LeWitt, Stuart Levy, Paul Miller (aka DJ Spooky), Marlena Novak, Joe Overstreet, Howardena Pindell, Richard Purdy, Tony Robbin, Dorothea Rockburne, Frank Rothkamm, Irene Rousseau, Carlo Séquin, John F. Simon Jr., John Sims, Clifford Singer, Kenneth Snelson, John Sullivan, Jack Tworkov, Roman Verostko, and Joan Waltemath.

One contribution from Sims was a visualization of pi’s digits, in a digital video format–with music by composer Frank Rothkamm and the participation of Paul D. Miller, who is better known on the New York City scene and elsewhere as DJ Snoopy.

In viewing the assembled artworks, carefully arranged to highlight similarities in theme, I was particularly struck by the diverse ways in which different artists can approach the same fundamental ideas, yet still reflect their mathematical essence. I also noted that nearly half of the artists represented in the show were unfamiliar to me–names to add to my already astonishingly long list of contemporary artists who find inspiration in mathematics.

The artworks were on display at the Selby Gallery from Feb. 22 to March 30, 2002. The show attracted a surprisingly large number of visitors, including a significant number of people who don’t routinely visit art galleries.

Dean and Sims are now interested in bringing a traveling edition of the exhibition to other locales and are looking for galleries that might be interested in hosting the show elsewhere in the country.

In addition to his classroom work and various art projects, Sims continues to seek ways to call greater attention to productive interactions between mathematics and art. He envisions starting up a glossy, accessible journal devoted to this form of art. Such a flagship publication would serve as a forum for the presentation and discussion of nascent and ongoing ventures and themes in mathematical art.

As the MathArt/ArtMath show clearly demonstrated, there is no paucity of material or interest in the topic.

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