50,000 folded business cards = one 3D fractal
September 11, 2012
An origami fractal made out of nearly 50,000 business cards is the first physical representation of the Mosely Snowflake three-dimensional fractal in the world. The sculpture was put together by more than 300 students and volunteers at the University of Southern California.
“Our community has brought this object into being for the first time,” said Catherine Quinlan, Dean of USC Libraries. “Before this project, this beautiful and enigmatic fractal existed only digitally and in the imaginations of mathematicians and artists.”
In mathematics, there's a little more to the concept of the fractal than the psychedelic computer-generated imagery with which we're all familiar. According to mathematician and "father of fractal geometry," Benoit Mandelbrot, a fractal is "a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension."
Mandelbrot's definition is a little like ancient parchment: very difficult to illuminate without committing vandalism, in this case to the subtlety and complexity of the idea. What's crucial is a property of the fractal that, actually, the computer visuals are rather adept at visualizing: their self-similarity at different scales. Get close up and what you'll see will strongly resemble the whole. The same is true of 3D fractals, physically manifest or otherwise.
The Mosely Snowflake fractal was discovered in 2006 by engineer and origami practitioner Jeannine Mosely, whose construction of the Menger Sponge fractal that same year (also out of business cards ... 66,000 of them) received widespread attention. The Menger Sponge was the first 3D fractal to be discovered, by Karl Menger in 1926.
If fractals had DNA, the Menger Sponge and the Mosely Snowflake would share an awful lot, but where the Menger Sponge is built from, and results in, cube shapes, the Mosely Snowflake generates broadly-hexagonal snowflake-like forms.
The effort to build an origami Mosely Snowflake has been led by Margaret Wertheim, co-director of the Institute For Figuring. “The snowflake fractal resides at the boundary of mathematics, engineering, and physical making,” Wertheim said, before adding that the origami Mosely Snowflake is representative of "a major international movement of art and mathematics."
However, the construction method was devised by Mosely herself, requiring a computer model to assess the number of business cards required (nearer 49,000 to be more precise) for the origami model to support its own weight.
Cards were assembled into thousands of cubes from which larger modules would be created, which would themselves require connection.
The Mosely Snowflake was put together for the 2011-2012 USC Libraries Discovery Fellowship, and will be on display from September 20 in the Doheny Memorial Library at USC's University Park Campus.
The video below, a guide with Jeannine Mosely, gives an idea of just how complicated construction of origami fractals can be, even at a relatively modest scale.