A 3-D fractal has taken physical form for the first time at the USC Libraries.
Fractals are geometric shapes in which the component parts resemble the whole. This quality, called self-similarity, results from repeatedly building up a form from small component units so that the overall pattern appears identical at all levels of magnification.
More than 300 USC students and faculty, Foshay Learning Center middle school students and other volunteers built the Mosely Snowflake Fractal out of nearly 50,000 folded business cards.
This collaborative community artwork is the culminating project of the 2011-12 USC Libraries Discovery Fellowship. Established by Dean Catherine Quinlan in 2011, the fellowship showcases the library as a place where disciplines intersect and where artists and scholars engage library collections and people to make possible surprising discoveries and creative works.
“Our community has brought this object into being for the first time,” Quinlan said. “Before this project, this beautiful and enigmatic fractal existed only digitally and in the imaginations of mathematicians and artists. It is an inspiring example of the creative potential that a great library makes possible for an entire community.”
Inaugural Discovery Fellow Margaret Wertheim spearheaded the project at the USC Libraries. Wertheim, also a science writer and curator, is co-director of the Institute for Figuring in Los Angeles and is known for the institute’s work on the Hyperbolic Crochet Coral Reef.
“The snowflake fractal resides at the boundary of mathematics, engineering and physical making,” Wertheim said. “Like a fantastic book, it opens your eyes to linkages between disciplines that are often kept far apart.”
Wertheim added: “Interdisciplinary exploration through mathematical origami has also been happening recently at the Japanese American National Museum and elsewhere in California. We’re truly experiencing an origami moment. With this enchanting fractal, the USC Libraries are on the forefront of a major international movement of art and mathematics.”
The Mosely Snowflake takes its name from engineer and pioneering origami artist Jeannine Mosely, who discovered its form in 2006 and designed the construction process.
“Once I figured out you could link cubes of folded business cards, I realized that you could actually build any structure, just anything you could imagine,” Mosely said. “So I started imagining things.”
In 2008, Mosely built a model of the Menger Sponge — a famous 3-D fractal discovered in 1926 by mathematician Karl Menger — out of 66,000 business cards. The snowflake fractal is closely related to the Menger Sponge form.
To plan the fractal’s construction at USC, Mosely coded a software simulation that allowed her to visualize the object, assess its structural integrity and calculate the required thickness and number of business cards.
Volunteers from the USC community then assembled thousands of the basic cubes. Others linked these cubes together to form more complex modules, which in turn were connected to create even more complex structures.
The modularity of the Mosely Snowflake Fractal is a “fantastic metaphor for what the USC campus is capable of achieving,” Wertheim said. “When you get hundreds of people putting their time and energy into building and linking these modules, you get a massively captivating structure. No individual could have achieved this.”
The exhibition will open on Sept. 20 at 5 p.m. in Doheny Memorial Library. Hand-drawn studies, digital renderings and items from the USC Libraries’ collections also will be on view.
The reception is free and open to the public. RSVP at usc.edu/esvp with the code “snowflake” or call (213) 821-1153 for information.
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