Fractal Roots and Artful Math

The term "mathematical art" for many people might conjure up images of M.C. Escher's endless staircases, Möbius-strip ants, and mind-boggling tilings. Or it might remind you 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 groundbreaking 2002 MathArt/ArtMath show at the Selby Gallery in Sarasota, Fla.

The realm of mathematical art is far wider and more diverse than many people realize, however. A groundbreaking 2002 exhibition at the Ringling College of Art + Design's Selby Gallery (now closed) 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, then director of the Selby Gallery, and John Sims, a mathematician and artist who taught at the Ringling School. Sims 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 remarked. "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).

Square Roots of a Tree. Courtesy of John Sims.

Tree Root of a Fractal, Sims noted, "shows how the latent geometry of nature can inspire and support abstraction." See also "Form Plus Function."

Sims brought the same sort of sensibility to the classroom. Mathematical ideas inspire artistic creations. Conversely, "to see mathematically, one draws from creativity and intuition, as in the case with the art process itself," he said.

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.

Holly's Rose: Artwork by Holly Brafflet as part of a course offered by John Sims at the Ringling School of Art and Design. Courtesy of John Sims.

It was a classroom journey, Sims said, 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."

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.

One ambitious scheme, Time Sculpture, involved installations scattered across the United States—familiar objects (vase, chess set, chair, clock, and so on) that are connected yet dispersed. Sims saw 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 original 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 assembled artworks, carefully arranged to highlight similarities in theme, exemplified the diverse ways in which different artists can approach the same fundamental ideas, yet still reflect their mathematical essence.

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 (see "Quilting Pi").

Originally posted June 10, 2002