The Complement of the Menger Sponge
The complement of an evolving Menger sponge is all of the material that has been removed so far.
Contents
Level zero
I described the Menger sponge fractal in this blog three weeks ago. At level zero, you begin with a solid cube of, say, gold.
Level one
Trisect 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 - 7 = 20 smaller cubes at level one.
Level one complement
The level one complement is all the material from level zero that was removed to obtain level one. I have made it a brighter shade of gold to provide contrast.
The union
The level one cube and its complement fit together nicely to recreate level zero.
Until next year
That's enough for now. I wanted to get to level one so I could use it my annual graphics-only holiday card.
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