Got spare business cards? Make a Menger Sponge!

Doctor Q

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A Menger sponge is a mathematical invention, a kind of fractal structure. To create one in 2 dimensions, divide a square into 3x3 sections, remove the middle section, then do the same for each remaining section: divide into 3x3, remove middle section, and so on. Doing that n times make a level-n Menger sponge.



Menger sponges aren't limited to a plane. They are equally well-defined in 3D or even higher dimensions.

The best part is that you can really see one: The Institute for Figuring is currently exhibiting a real, 3-dimensional level-3 Menger sponge built by Dr. Jeannine Mosely and a team of volunteers.

Dr. Mosely has a degree from M.I.T., works in 3D modeling, studies computational Origami, and has created this Menger sponge completely out of folded business cards! Now why didn't I think to do that? :cool:

Facts about the business card Menger sponge:
66,048 business cards
dimensions 54"x54"x54"
weight 150 pounds
time to build: 9 years!​

Dr. Mosely and the Menger sponge:



If you are geeky enough (like me) to think this was a worthwhile project, here are some more photos you can admire. :)
 

After G

macrumors 68000
Aug 27, 2003
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Getting paid to build a Menger sponge for 9 years ... dream job? :D

I guess not so dreamy for the volunteers though. :p

And yes, I know she did other things during that time. :)
 

SamIchi

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Aug 1, 2004
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That's very cool. So it takes 6 business cards to make one of those cubes?
 

Doctor Q

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She says that a level-4 Menger sponge made from business cards would collapse under its own weight. It would be much bigger and take much longer to build. Who wants to help me prove her wrong? ;)
 

SamIchi

macrumors 68030
Aug 1, 2004
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Doctor Q said:
She says that a level-4 Menger sponge made from business cards would collapse under its own weight. It would be much bigger and take much longer to build. Who wants to help me prove her wrong? ;)
I'm in!
 

Doctor Q

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Great. We can all meet at the lecture Dr. Mosely will be giving this Sunday at 8pm on "Structural Considerations of the Business Card Sponge".

The exhibit is at the Machine Project gallery near downtown Los Angeles (map).

If you want to make a level-1 Menger sponge out of 192 business cards, follow these instructions (pdf).

If you want to read more about computational Origami, here is a good article with photos.
 

knackroller

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Feb 28, 2006
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Seems to be a pretty low level sponge for such a highly qualified person..............
 

Doctor Q

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knackroller said:
Seems to be a pretty low level sponge for such a highly qualified person..............
What I found interesting is that she seems to understand all aspects of the mathematics and the construction technique, but she grossly underestimated the time required to build this model. Why?