THEMOSELYSNOWFLAKESPONGE LEVEL ONE
A USC LIBRARIES DISCOVERY FELLOW PROJECT AT THE INTERSECTION OF MATHEMATICS, ART, AND LIBRARIES
In 1926, mathematician Karl Menger discovered the first three-dimensional fractal, which came to be called, in his honor, the Menger Sponge. Eighty years later Dr. Jeannine Mosely, an MIT-trained engineer, built a model of this extraordinary object using 66,000 business cards.
Now Dr. Mosely has discovered a relative of Menger’s original fractal—the Mosely Snowflake Sponge. USC Libraries Discovery Fellow Margaret Wertheim and Dr. Mosely are leading the USC community in constructing this unique mathematical form out of 49,000 business cards. This is the first time in the history of the world, and perhaps the universe, that this wondrous fractal object will be brought into being.
These instructions describe how to assemble a level one Mosely Snowflake Sponge, a smaller variant of the level three fractal under construction at USC. Additional information as well as instructional videos are available online at www.usc.edu/libraries/sponge.
ABOUT JEANNINE MOSELY A graduate of MIT with a Ph.D. in electrical engineering and computer science, Mosely has pursued a career in three-dimensional modeling software. She is well-known for her Business Card Menger Sponge, a large-scale, participatory, origami project that engaged hundreds of people across the USA. Mosely believes that folding origami structures is a way of giving life to mathematical theorems and formulae. Her recent work focuses on folding curved lines in modular forms and tessellations. She designed and developed the methods for creating the Mosely Snowflake Sponge.
ABOUT MARGARET WERTHEIM Margaret Wertheim is a science writer, curator, and the author of books on the cultural history of physics and perception. In 2003, she and her twin sister Christine founded the Institute For Figuring, a Los Angeles-based organization that explores the poetic and aesthetic dimensions of science and mathematics. In 2011, she became the USC Libraries inaugural Discovery Fellow. Her most recent book—Physics on the Fringe: Smoke Rings, Circlons, and Alternative Theories of Everything—was published in October 2011 by Walker & Co.
ABOUT THE USC LIBRARIES DISCOVERY FELLOWSHIP Dean Catherine Quinlan established the Discovery Fellowship in 2011 to encourage students and scholars to engage library collections in inventive and surprising ways. As the libraries’ first Discovery Fellow, Margaret Wertheim has curated The Marine Sublime—an event that explored the relationship among art, marine biology, and rare scientific works in the libraries’ special collections— and a discussion and workshop that investigated the mathematical character of Lewis Carroll’s Alice’s Adventures in Wonderland. With Jeannine Mosely, she is leading the Snowflake Sponge project at USC. www.usc.edu/libraries www.usc.edu/libraries/sponge
MAKINGTHELEVELONESPONGE EACH LEVEL ONE SPONGE REQUIRES 108 STANDARD BUSINESS CARDS
HOW TO MAKE CARD CUBES
1. 2. 3. 4.
5. 6. 7. 8.
9. 10. 11.
1. Place one business card across another, centered and at right angles to the first.2. Fold the flaps down as shown.3. Separate the cards. Make 6 for each cube. 4. Assemble the cards so that all the flaps are on the outside, matching short edges to long edges. 5-8. Adding each of the 6 cards to complete the first cube. 9-10. Link 2 cubes together by slipping a flap from one cube under the corners of 2 flaps on an adjacent cube, then slip the matching flap from the first cube under the other 2 corners of the flaps on the second cube. 11. Link a third cube to form a 3-cube rod.
COMBINING CUBES TO MAKE A LEVEL ONE SPONGE
1. 2.
3. 4. 5. 6.
1-2. Make three cubes. 3-6. Make 4 rods of 3 cubes. Note the orientation of the flaps. Two of the middle faces should have horizontal flaps, the other two should have vertical flaps. MAKINGTHELEVELONESPONGE EACH LEVEL ONE SPONGE REQUIRES 108 STANDARD BUSINESS CARDS
COMBINING CUBES TO MAKE A LEVEL ONE SPONGE
7. 8.
9. 10. 11.
7. Link the 2 single cubes to one of the rods to form a U shape. 8. Attach the U module to a rod of three cubes as shown. Swing the U and the rod together and slip the marked flaps under the neighbor’s flaps as indicated by the arrows. 9. Eight linked cubes. 10. Add another rod of 3 cubes. 11. Add the fourth rod of 3 cubes. 12. Build 4 additional cubes into vacant midsections (A-D below) so that all 6 faces form a cross. 13. The finished Level One Mosely Snowflake Sponge.
A
B
C
D
12. 13.