The MegaMenger may be the largest fractal ever built, made out of over a million business cards. Creating the MegaMenger involves building Menger Sponges, three-dimensional fractal cubes made from 20 smaller identical fractal cubes.
A Menger Sponge is a three-dimensional fractal, which can be made by taking a cube and cutting out a square section through the centre in each of the three directions; then each of the resulting smaller cubes is cut out in the same way, and so on until you've removed infinitely many pieces. So each Menger Sponge is made from twenty identical-but-smaller Menger Sponges. This results in an object which has zero volume but infinite surface area!
Volunteers helped build 8,000 small cubes out of nearly 50,000 business cards. These were combined in groups of 20 to create 400 level one Menger Sponges.
The level one sponges were combined in groups of 20 to make 20 level two sponges, which then formed a massive level three Menger Sponge. The resulting fractal cube was over one and a half metres tall and can be seen in the atrium of 4 West.
Twenty level three Menger Sponges, made around the world, will now come together to form a level four sponge, the largest fractal structure ever made out of business cards.
Organiser Ben Sparks said: “The aim is partly to see if it can be done, and partly to grapple with some good maths in a very physical way. It's a nice example of where maths meets art, and it's also a great opportunity for people to get together, do some hands on maths and have some fun.
"It's been an amazingly successfully week. We've had primary students building with maths professors, undergraduates and postgraduates mixing with secondary school pupils, and students mixing with university staff all week - including the Vice-Chancellor - all discussing maths while building cubes.”