Monday, October 18, 2010

Level One Menger Sponge

"In mathematics, the Menger sponge is a fractal curve. It is a universal curve, in that it has topological dimension one, and any other curve (more precisely: any compact metric space of topological dimension 1) is homeomorphic to some subset of it. It is sometimes called the Menger-Sierpinski sponge or the Sierpinski sponge. It is a three-dimensional extension of the Cantor set and Sierpinski carpet. It was first described by Karl Menger (1926) while exploring the concept of topological dimension."

This specific model is made out of 120 Sonobe units.

I chose two complimenting colors and folded 72 of one color (silver) and 48 of the other (blue).  The different colors are almost identical.  The only difference is the side of the module that is folded.  Example below:

Note: Foil is highly overrated for origami.

A bunch of modules waiting to be assembled.

I first encountered the Sonobe unit in the book "Modular Origami Polyhedra".  It's a good book with a lot of neat models in it.  Assembling the cube is easy, but time consuming.  Alternate the colors and I recommend making one full side first and building up from there.

Keep adding the modules.  Just keep building, just keep building and eventually you will be rewarded with the completed model.  One level one Menger sponge.

There you go, the final model.   Took about a day to complete working on it slowly. ^_^

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