# Mathematics Weblog

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## Menger Sponge

Wednesday 2 August 2006 at 3:00 pm | In Articles | 4 CommentsMaths *can* be fun. Students at Cornell College in Iowa have built a 3-dimensional fractal called a Menger Sponge and you’ll find a video and pictures of how they did it here.

Menger sponge |

*Thanks to Mathforge for the link*

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Is it possible to do something similar on an n-cube for n>3 ?

There’s no mention of that in the wiki article so maybe I’m missing something obvious (do n-dimensional fractals exist in general?).

Comment by Craig — Saturday 5 August 2006 7:58 am #

Yes – it is possible. There’s a 4D HyperGasket which also says:

By following the procedure of creating a gasket in the 2nd and 3rd dimensions it is possible to do the same thing in higher dimensions, in particular the 4th dimensionand the recipe for a 4D version made from a hypercube is at Hyperspace Travel Guide. These are really just Cantor’s Set in higher dimensions so it is easy to see how it can be done there.

A picture of a stage-6 Menger Sponge can be found at Hexahedron Fractal. It is interesting to record that the Menger Sponge has dimension 2.73 (more precisely ).

Comment by Steve — Saturday 5 August 2006 10:26 am #

A ha! Thanks for the links. Yes, it’s interesting to note that what you intuitively think of as a 3-dimensional thing is actually 2.73 dimensional and so on for higher dimensions.

Comment by Craig — Sunday 6 August 2006 7:39 am #

Thanks for the video, I will most likely pass the link along to my students.

Comment by DRR — Tuesday 8 August 2006 1:54 am #