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Menger Sponge

I made an origami approximation to a Menger sponge.

This was most of my day. A Menger sponge is a three-dimensional fractal shape, where the middle of each face of a cube is removed like in the origami shape here and then each of the remaining 20 cubes are reduced in the same way, and so on ad infinitum.

A cube has six faces. This origami shape has 72. The next shape in the series has over 1000. I have a scary urge to try to make it. In a quick not-even-back-of-the-envelope calculation, it wouuld take me about two months.

Comments:
Mon, 02nd Oct 2006 (09:28)

I made this when i saw your post this morning. It's not quite right, but I'm sure it will suffice. Maybe I will build the next shape up aswell… Then we can combine them to make a menger-house!

http://jamieoleary.net/gallery/origami/pseudomentri.jpg

I need coffee..

by Jamie O'Leary
Mon, 02nd Oct 2006 (12:50)

I wouldn't like to live in a Menger house. It would have infinite surface area so it would be a bitch to paint.

by Rory
Mon, 02nd Oct 2006 (14:44)

you may as well start now. that way when you eventually decide to make it, you'll already have started…

by Sj
Wed, 04th Oct 2006 (10:55)

Well, painting it would be the least of your problems. Presumably the material used to construct the surfaces would have some finite mass per cm^2. This would mean that your house would be infinitely massive, and I think you might find it hard to get paper that can support an infinite amount of mass (actually I think you'd be hard pressed to find paper that could withstand the gravitational field gradient).

by Joe
Wed, 04th Oct 2006 (10:59)

That sounds like a challenge to me…

Alright everybody, to muji for paper supplies! I need ALL the paper. It's time to show physics that triangles don't follow the rules.

by Jamie O'Leary

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This piece was posted on Mon, 02nd Oct 2006 at 00:52. It is tagged with .

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