Monday, September 24, 2007

Slice of Menger sponge

Slice of Menger
Originally uploaded by Seb Przd
What happens when you slice a Menger Sponge diagonally through the center? well, a very interesting pattern of stars and hexagons. This is the level four iteration on the Menger sponge.

I haven't seen this mentioned before on the internet. Maybe a reader will know if these intersections of the Menger Sponge have been studied before? Wolfram mentions that:
The Menger sponge, in addition to being a fractal, is also a super-object for all compact one-dimensional objects, i.e., the topological equivalent of all one-dimensional objects can be found in a Menger sponge (Peitgen et al. 1992).


At 2:09 AM, Blogger mike said...

If you slice a grid of cubes with a plane whose slope is (sqrt(5)+1)/2 in one direction and (sqrt(5)-1)/2 in the other direction, you get Penrose tiles. What happens to the Menger sponge?


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