Creating the world’s largest fractal one fold at a time

GV students and professors help construct MegaMenger

By Carly Simpson | 10/26/14 10:18pm

Last week, fingers were flying in Mackinac Hall at Grand Valley State University as dozens of mathematics students and professors helped build what may be the largest fractal ever built, the MegaMenger.

GVSU’s mathematics and statistics club partnered with Calvin College to make Grand Rapids one of 20 sites worldwide participating in the MegaMenger project.

“About a month ago, we were contacted by professor Randy Prium, who is a math professor at Calvin College,” said Edward Aboufadel, a math professor at GVSU. “Calvin had volunteered to be one of the 20 international sites for the Menger build, and he asked us to be a partner. This seemed like a good activity to build community in our mathematics department, so we decided to contribute.”

Using business cards, students and professors created a paper sculpture of Menger’s Sponge, a cubic representation of a fractal, a never-ending geometric pattern that repeats on all scales. The sponge is named for its inventor Karl Menger.

The MegaMenger Build included participants from countries such as Spain, China, New Zealand and Finland. The volunteers used over one million business cards to create the model fractals.

“I think this is a great activity – making math real,” Aboufadel said. “I don’t know of other fractals that have been built, so I can’t compare, but you don’t see fractals of this size very often. Usually, fractals are just two-dimensional and generated on a computer. It is unusual to create a 3D fractal.”

It takes 120 business cards to make a Level-1 Menger Sponge, which is composed of 20 cubes arranged in the shape of a larger cube with holes cut through the middle in each direction.

A Level-2 sponge is composed of 400 cubes, and a Level- 3 sponge is made of 8,000.

Each of the 20 building sites were responsible for creating one Level-3 sponge, which would then form a distributed Level-4 sponge, the largest ever made out of business cards. Each location built their level-three sponge during the week of Oct. 20-26.

“There were a few professors that had their classes work on the project, and other people brought some of the cards home to do it with their families, and in one case, a cub scout troop,” Aboufadel said.

A Level-1 sponge takes two to three hours to make, Aboufadel said. Participants at GVSU made 20 and then joined them together on Friday, Oct. 24 to create a Level-2 sponge, which will be connected with the model at Calvin College.

The MegaMenger project was sponsored by Queen Mary University of London, the Manchester Science Festival and the Museum of Mathematics (MoMath) in New York.

For more information, visit To see pictures, checkout #megamenger on Twitter.

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