Union contributes to world’s largest fractal in honor of Martin Gardner


By Song My Hoang

Economics Professor Mary O’Keefe organized a diverse group of volunteers to participate in the MegaMenger project, which is a distributed worldwide fractal build that spans 20 international sites.

The group of fractal builders includes Union students, staff and alumni as well as middle and high school students from the Science Technology Entry Program (STEP), members of the Albany Area Math Circle and students and faculty from University of Albany, Schenectady County Community College and Rensselaer Polytechnic Institute.

A fractal is a naturally occurring phenomenon or mathematical set that shows repeating patterns that are displayed at every scale. The MegaMenger is composed of Menger Sponges, which are three-dimensional fractals that can be made from cubes attached together.

According to the MegaMenger website, each cube is made by cutting out a square section through the center in each of the three directions to make a Level 0. A Level 1 consists of 20 single cubes made from business cards.

Twenty Level 1 sponges make a Level 2 sponge and 20 Level 2 sponges create a Level 3. The resulting fractal cube will be one-and-a-half meters tall.  By the end of the project, each site will have built 8,000 small cubes out of nearly 50,000 business cards.

Each site will construct a Level 3 sponge; the compilation of 20 Level 3 Menger Sponges will form a distributed Level 4 sponge, which will become the largest fractal built out of business cards.

This process results in an object that has zero volume but infinite surface area.

Currently, 11 of the international Level 3 build sites have finished constructing a Level 3 Menger Sponge, including the Museum of Mathematics located in Manhattan.

O’Keefe led the Union and local community to contribute a Level 2 sponge, which is currently placed in the Museum of Mathematics in New York City. The group finished the Level 3 Menger Sponge in Schaffer Library on the evening of Friday, Oct.  24.

O’Keefe, Susan Beckhardt ’08, STEP students and STEP mentors Andrew Guyatt ’17 and Sophia Powell ’17 travelled to New York City to deliver their finished Level 3 sponge as well as help other groups strengthen their sponges.

“Our level 2 fractal component was considered to be one of the strongest by project director Laura Taalman, and, therefore, she selected it to be one of the four cantilevered components of the fractal’s roof,” O’Keefe mentioned.

O’Keefe has been organizing “Guerilla Math Circles,” which involves working with underprivileged students to go to the sidewalks and draw mathematical patterns with chalk. She noted, “People don’t know we are doing math. They come up and ask what we are doing and wonder if they could do it too.”

Guerilla Math Circles is a way to spread the idea that math is a beautiful subject.

“Math is everywhere. For example, there is math in different cultures. There is a program at RPI that specializes in looking at African mathematics. Fractals turn out to be in African textile weavings, patterns in thatched roofs and cornrow braiding,” said O’Keefe.

O’Keefe emphasized the serendipity of this method of learning.

She shared that their train to Manhattan was delayed for half an hour, so she came up with a spontaneous math project.

In the process, an older woman overheard their conversation and became interested in the project. The woman told O’Keefe that she appreciated O’Keefe’s work and would love to bring it home to share with her children.

Another example was when O’Keefe’s colleague from the Economics Department brought his thesis student to participate in the MegaMenger project. The student realized that he could incorporate the MegaMenger project in his senior thesis.

As the weather became colder, O’Keefe wanted to provide an alternative to drawing on the sidewalks. Therefore, she was excited to participate in the global fractal-building project.

The idea was to complete the project within the past week, as it would have been mathematical writer Martin Gardner’s 100th birthday, if he were still alive. O’Keefe mentioned that Gardner was well known for translating mathematical concepts to the public; he wrote a monthly column for Scientific American. She explained that his works are influential and have become an inspiration for various mathematicians.

O’Keefe added examples of individuals who were influenced by Gardner, “A professor at MIT grew up in a rural part of Italy, where nobody cared about education and the idea of women getting an education was unthinkable. She had access to these articles in the magazine and became inspired.”

“Another professor who teaches at Siena College and grew up in a remote part of Iran claimed to have become a world-class mathematician because of Gardner,” O’Keefe continued.

O’Keefe further added that the MegaMenger project was an act that symbolized the fact that all the mathematicians around the world are grateful for Martin Gardner.

She wanted Union to be involved in this global endeavor. “That’s why it was so cool that the library welcomed us to use their learning space. People would be curious and stop by to join the building process. I’m grateful to the library for welcoming and encouraging us to use the space,” O’Keefe noted. Union’s Level 2 Menger Sponge will temporarily be at the Museum of Mathematics.

O’Keefe hopes to bring the structure back to Union to put it on display.

O’Keefe concluded, “This MegaMenger project exceeded my wildest dreams … I ended up with a team of people who are heavily invested in the project.”


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