Calvin participates in worldwide fractal construction project
Dr. Randall Pruim’s fingers fly as he folds business cards into dozens of paper cubes. Over the next week, Pruim and other volunteers will assemble thousands of such cubes into a model of a Menger sponge fractal.
Calvin College is one of 20 sites worldwide participating in the MegaMenger project. Sponsored by Queen Mary University of London, the Manchester Science Festival and the Museum of Mathematics (MoMath) in New York, MegaMenger aims to fashion model fractals from more than a million business cards in total.
A Menger sponge is a mathematical object known as a fractal, a geometric figure that contains many self-similar features on multiple levels, often involving an infinite process. Each level of a Menger sponge can be thought of as a cube built out of 20 smaller cubes, each of which are built out of 20 smaller cubes ad infinitum.
The model Mengers are constructed from base cubes made of six business cards each. Twenty base cubes can be joined into a level one cube. Twenty level one cubes form a level two cube, measuring about one-and-a-half feet across. Calvin’s goal is a level three cube, which will require about 50,000 cards, weigh 170 pounds and measure about 4.5 feet across.
“It’s basically a modular origami,” said Pruim, who is chair of the mathematics and statistics department. Pruim is leading Calvin’s Menger building effort.
“The idea that you can take these little folded pieces of paper and build a 3D structure out of them is pretty neat,” said Peter VandeHaar, a senior biochemistry and computer science student. “It’s really enjoyable, just sitting around and making these and building something interesting out of them.”
VandeHaar has become a student leader in the build effort. Accompanying Pruim at training sessions, he has been involved with teaching, quality control and higher-level assembly. Putting together higher-level cubes “takes a lot more finesse,” said VandeHaar.
“The biggest thing is we need people to come build,” said Pruim.
A level three cube takes an estimated 1000 person-hours to build. Pruim invites dorms and student organizations to “adopt” a portion of the structure.
Calvin is not without help. The Grand Valley State University Mathematics and Statistics Club and Grand Rapids Christian Middle School are building sections which will be incorporated with Calvin’s.
Public build sessions will take place in the Fieldhouse on Friday, Saturday, Tuesday and Wednesday of this week. Volunteers at these sessions will create level two cubes that will be assembled into the final level three cube on the second floor of North Hall. There, the MegaMenger will serve as a permanent art installation for the math department.
The art and art history department and the science division have joined math to sponsor the event.
“The event’s slogan, ‘Math + Art + You = Mega Menger,’ emphasizes that there’s some math to it and some art to it, but we also need a lot of participation to make this happen,” said Pruim.
“It’s really fun to see people get excited about this,” said VandeHaar.
“There’s no mathematical prerequisites if you want to volunteer,” emphasized Pruim. “It’s kind of like a participatory art project at ArtPrize where you get lots of people involved and something comes together over the course of a week.”
Constructing Calvin’s MegaMenger is an exercise left to the reader.
Public build sessions will happen in the Spoelhof Fieldhouse on Friday, October 17 from 4 p.m. to 9 p.m.; Saturday, October 18 from 1 p.m. to 5 p.m.; Tuesday, October 21 from 4 p.m. to 9 p.m. and Wednesday October 22 from 4 p.m. to 9 p.m.
More information can be found on the Calvin mathematics & statistics department MegaMenger website.