San Francisco - Adding a new dimension to mathematically-inspired art, Carlo Séquin has developed computer programs that generate elegant sculptures based on mathematics found in the curving shapes of soap bubbles.
The University of California, Berkeley, computer science professor's foray into art was inspired by the graceful geometrical wood forms of Missouri-based sculptor Brent Collins. Séquin will demonstrate the computer program, and Collins will describe his sculptures, on Friday, Feb. 16 at the annual meeting of the American Association for the Advancement of Science in San Francisco.
The scientist and the sculptor became acquainted after
Séquin noticed Collins' work in a 1992 issue of the art
journal Leonardo. Collins' sculptures of intertwined arches
and saddles were conceived through artistic intuition, not
mathematical principles, yet they exhibit the grace and
balance of the saddle-shaped "minimal surfaces" that soap
films form as they stretch within twisted wire loops.
These shapes have long fascinated mathematicians because they represent the smallest area the film could occupy given the constraints of its borders. "To simulate these surfaces involves billions of computations, and yet nature does it so easily," said Séquin.
Séquin contacted Collins to discuss his sculptures and propose new, more complex constellations of saddles. When he learned that for each new idea Collins first painstakingly fashions a prototype from wire mesh and beeswax, he suggested the use of a computer program to visualize novel shapes in a fraction of the time it takes to build the prototypes. A few months of programming by Séquin and his students yielded computer software that generates Collins-style sculptures in the form of a stack of simple saddles bent to form a circle.
During the following year, Séquin gradually enhanced the program to produce sculptures with higher-order saddles that have three or more valleys between an equal number of upward-curving slopes. The program's user-friendly interface makes it easy to experiment with the number of saddles and holes, the number of valleys in the saddle, the amount of twist, various textures and colors as well as other parameters. More recently, he adjusted the program to produce intertwined loops of saddles - shapes impossible for Collins to conceive or build with his traditional approach.
When both parties agree that a new form is worthy to become a physical sculpture, Séquin's program slices the geometrical shape at 7/8-inch-wide intervals and creates a set of full-size blue prints for the various cross sections at different levels of the sculpture. Collins then uses these computer drawings as templates to pre-cut 7/8-inch wood boards into convoluted shapes, which, when properly stacked on top of one another, form the new sculpture. After a month of grinding and sanding, a beautiful smooth shape with a satiny finish emerges, as exemplified by Collin's "Hyperbolic Hexagon II."
Both artist and computer scientist have benefited from the collaboration. Collins can choose from a number of very complex prototypes before beginning a new project. Séquin uses the artistic shapes to teach his students the principles of computer-aided design and rapid prototyping. His laboratory now has a Fused Deposition Modeling machine in which small models can be fabricated within a couple days. These artistic endeavors illustrate the use of computers for more than just menial computation, said Séquin. "When used in such an interactive mode," he said, "the computer becomes an amplifier for the creative process."