Friday, September 01, 2006

Building a Menger Sponge

theifforg reports: [edited]

Menger's sponge - named for its inventor Karl Menger (1902-1985) and sometimes wrongly called Sierpinski's Sponge - is a fractal solid that can be described as follows. Take a cube, divide it into 27 (3 x 3 x 3) smaller cubes of the same size; now remove the cube in the center of each face plus the cube at the center of the whole. You are left with a structure consisting of the eight small corner cubes plus twelve small edge cubes holding them together. Now, imagine repeating this process on each of these remaining 20 cubes. Repeat again. And again, ad infinitum...

The Business Card Menger Sponge Project

The primary goal of the Business Card Menger Sponge Project was to build a depth 3 approximation to Menger’s Sponge as shown above, out of 66,048 business cards. This can be done by building 8000 business card cubes of 6 cards each, linking them together and using the additional cards to panel the 18,048 exterior faces of the sponge, giving a more pleasing finish to the final structure.

In order to build the sponge, I devised a decomposition of the overall structure into simple units that almost anyone can learn to make, which can then be assembled into the whole. The finished sponge measures slightly over 54 inches (140 cm) on each side and weighs about 150 pounds (70 kg).

My idea was that a model of a level 3 Menger Sponge would be built out of business cards one cube at a time, with many folders helping by pre-creasing the business cards. As the structure got larger there would be room for perhaps as many as 4-8 people to work on it simultaneously. They would still be the major bottle neck, since assembly and paneling alone take more than half the construction time. I calculated it would take such a group working together around 50-100 hours from start to finish, but I doubted I could find enough dedicated volunteers to do it this way...

Visit this page for more information than you will ever need about building your own Menger Sponge.

For information about the Institute for Figuring visit their about page.


Skep said...

Definitely VERY cool. A good effort, at least... shame he didn't continue it on to infinity though... XD

David Makin said...

Slightly closer to infinity, but virtual:

Dave Makin