Menger sponge instructions
What is a Menger sponge?
The Menger sponge is a fractal, incorporating self-similarity—that is, there are component parts of the Menger sponge that are rescaled versions of the entire object. Many natural phenomena have fractal characteristics, among them plants, clouds, and mountains.
To build a Menger sponge, start with a block of 27 cubes, and remove the 6 cubes at the center of each face and the cube at the very center of the block. The 20 cubes that remain form the level 1 Menger sponge. To build the level 2 Menger sponge, take a level 1 Menger sponge and replace each of its 20 cubes with a 1/3 scale level 1 Menger sponge. This process can be repeated: to form the level n + 1 Menger sponge, take a level 1 Menger sponge and replace each of its 20 cubes with a 1/3 scale level n Menger sponge. The Menger sponge is the limit of this process.
Examples of Level 1 and Level 2 business card Menger sponges are on display in the lobby of the Williams Center. The Lafayette Level 3 Menger sponge will be constructed of 8,000 business card cubes—48,000 cards for the cubes, and 18,000 for paneling. The finished size will be a 54 x 54 x 54 inches.
Sponsors are Minuteman Press and Lafayette’s Reprographics office, along with Naaci Printing of Bethlehem and Harmony Press of Easton.