August 8, 2008

A Tetrix at Burning Man

Burning Man is an eccentric cultural gathering, a celebration of community and self expression, held annually in the Black Rock Desert of Nevada. Tens of thousands of participants immerse themselves in a week of art, music, theater, technology, and social activism, while camping out on the playa. The event climaxes with the burning of a giant sculpture, the Man.

In recent years, several installations and camps at Burning Man have had a mathematical flavor. The 2003 edition, for example, featured a contorted Möbius-strip jungle gym. Tom Davis, formerly principal scientist at Silicon Graphics, has web pages describing activities at several Burning Man gatherings, including a rudimentary "math camp" in 2007.

This year's Burning Man will be held Aug. 25 to Sept. 1, and mathematician and beadwork artist Gwen L. Fisher of California Polytechnic State University in San Luis Obispo is working with Paul Brown on an adult-sized jungle gym in the form of a Sierpiński tetrahedron (or tetrix) for the event.

The sculpture, called "Bat Country," will stand 21 feet tall and be built from 384 aluminum baseball bats, which form the structure's edges, and 130 12-inch softballs, with one ball at each vertex. It consists, essentially, of 64 tetrahedra. Steel rods, which thread the bats, stabilize the structure.

Based on a fractal structure known as a Sierpiński tetrahedron, "Bat Country" will consist of 64 tetrahedra made from aluminum baseball bats connected by softballs. Courtesy of Gwen Fisher.

"Bat Country" was inspired by Fisher's most popular three-dimensional beaded sculpture, an elegant assemblage of seed beads, bugle beads, and thread. Three views of this beaded fractal framework appeared on the cover of the June 2007 Journal of Mathematics and the Arts, accompanying an article by Fisher and Blake Mellor on the symmetries of beaded beads.

Fisher and her coworkers have now assembled the components into one of the four units that will make up the jungle gym and tested its stability, in preparation for installation at Burning Man 2008.

Fisher stands atop one of four tetrahedral units that will make up the "Bat Country" jungle gym. Courtesy of Gwen Fisher.

Fisher notes that the sculpture looks dramatically different from different points of view. From the outside on the ground, "Bat Country" looks like a triangle with a complex lattice of interior edges, she says. From certain angles, however, the bats align, and the structure appears to be a two-dimensional Sierpiński triangle. Looking upward, a viewer can see intriguing arrays of diamonds or triangles.

Looking upward from inside "Bat Country," reveals a symmetric array of triangles. Courtesy of Gwen Fisher.

After Burning Man, Fisher and Brown hope that their sculptural jungle gym can go on public display in the San Francisco area.

No comments: