How many business cards are needed to complete a level 3 Menger Sponge? What is a level 3 Menger Sponge? Tim Chartier, author of Math Bytes: Google Bombs, Chocolate Covered Pi, and Other Cool Bits in Computing, explains.
In a Huffington Post article, A Million Business Cards Presents a Math Challenge, Chartier asks readers to go in their wallet and check for business cards. If there aren’t any, “they may be part of a worldwide math challenge. Over the past month, people around the world have been building a mathematical structure out of more than a million business cards.” That mathematical structure is a Mega Menger, but before we get there, let’s discuss what a level 1 Menger Sponge is.
A level 1 Menger Sponge is a fractal consisting of twenty cubes. Each cube is made up of 6 business cards, so a level 1 Menger needs 120 business cards. A level 2 Menger is created using 20 level 1 Mengers, a level 3 Menger is made with 20 level 2 Mengers, so on and so on.
Here at the Press, we don’t have a million business cards to complete a Mega Menger, but we do have a lot of books. Using Chartier’s code (which you can play with here: http://lifeislinear.davidson.edu/sierpinski.html), we were able to create 2-D versions of a Menger Sponge called a Sierpinski Carpet using our jacket images. Below, see if you can figure out which books are featured in the fractal images below! Click the images to see the related title.