The Complement of the Menger Sponge - Cleve Moler on Mathematics and Computing

[poster]

The complement of an evolving Menger sponge is all of the material that has been removed so far.

ContentsLevel zeroLevel oneLevel one complementThe unionUntil next yearLevel zeroI described the Menger sponge fractal in this blog three weeks ago. At level zero, you begin with a solid cube of, say, gold.



Level oneTrisect the level zero cube into 3x3x3 = 27 smaller cubes, like a Rubik's cube without the labels. Remove the center cube from each of the six faces, as well as the cube at the very center. This leaves these 27 -



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