## Works by John M SullivanBorromean Rings | Minimal Flower | Unknotworks in situ
John M. Sullivan was born in 1963 in Princeton, NJ, USA. After earlier degrees from Harvard and Cambridge Universities, he received his Ph.D. in Mathematics from Princeton in 1990. He was then a postdoctoral fellow at the Geometry Center, and taught at the University of Minnesota. In 1997 Sullivan took a new faculty position at the University of Illinois, Urbana. In 2003, he moved to Berlin, where he is Professor of Mathematical Visualization at TU Berlin. Sullivan's mathematical art -- prints and sculptures generated by computer -- has been exhibited in Manhattan, Bologna, Massachusetts, Ohio, and Paris. "My art is an outgrowth of my work as a mathematician. My research studies curves and surfaces whose shape is determined by optimization principles or minimization of energy. A classical example is a soap bubble which is round because it minimizes its area while enclosing a fixed volume. Like most research mathematicians, I find beauty in the elegant structure of mathematical proofs, and I feel that this elegance is discovered, not invented, by humans. I am fortunate that my own work also leads to visually appealing shapes, which can present a kind of beauty more accessible to the public. John Sullivan can be reached at jms@isama.org. ## Borromean RingsJohn M Sullivan, Stuart Levy, Ken Brakke, Jeff Carpenter, 1998 immersive interactive application Three rings, so linked that if one is broken, the other two come apart as well, can be placed in a spatially symmetric way. But, this is not the only position of least energy. The other, nearly planar, minimal position will be familiar to fanciers of Ballantine's Ale. Animation: Stuart Levy Dynamics: John M Sullivan Evolver Software: Ken Brakke Post-Production: Jeff Carpenter From "Knot Energies," ICM Berlin, 1998 top ## Minimal Flower 3John M Sullivan, original 2001, reprint 2006 ZPrinter Z406 printed plaster sculpture Minimal Flower 3 is an homage to Brent Collins, whose sculptures have been very inspirational to me. For this sculpture, I designed the boundary curve and an initial surface by hand, and then used software to model a minimal surface. This, mathematically, is the optimal shape a soap-film spanning across the boundary would achieve. The geometric equilibrium of a minimal surface, where the curvatures of the surface always balance in a saddle configuration, adds to its beauty."
top ## UnknotJohn M Sullivan, Stuart Levy, Ken Brakke, Jeff Carpenter, 1998 immersive interactive application Not every tangled mess of a string tied into a loop is knotted. Putting a virtual repulsive charge on the string, a computer can untangle this unknot into the obviously unknotted circle without breaking the loop. It does this by reducing the energy induced by this charge. Animation: Stuart Levy Dynamics: John M Sullivan Evolver Software: Ken Brakke Post-Production: Jeff Carpenter From "Knot Energies," ICM Berlin, 1998 top About | Works | In Situ | Technology | Contact | |

The Traveling CANVAS is developed by the ISL at the Beckman Institute at the University of Illinois at Urbana Champaign. |