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- Sierpinski Carpets 27 answers
My challenge, is for you to generate a Menger Sponge based on the
iteration given. You need to draw it in
3d, anyway you can.
0, 1, 2, 3
What is a Menger Sponge
In mathematics, the Menger sponge (also known as the Menger universal curve) is a fractal curve. It is a three-dimensional generalization of the Cantor set and Sierpinski carpet
See https://en.wikipedia.org/wiki/Menger_sponge#Properties (too long to copy and paste)
How do I construct the sponge?
Begin with a cube (first image).
Divide every face of the cube into 9 squares, like a Rubik's Cube. This will sub-divide the cube into 27 smaller cubes.
Remove the smaller cube in the middle of each face, and remove the smaller cube in the very center of the larger cube, leaving 20 smaller cubes (second image). This is a level-1 Menger sponge (resembling a Void Cube).
Repeat steps 2 and 3 for each of the remaining smaller cubes, and continue to iterate ad infinitum.
The second iteration gives a level-2 sponge (third image), the third iteration gives a level-3 sponge (fourth image), and so on. The Menger sponge itself is the limit of this process after an infinite number of iterations.
Background info taken from this wikipedia page on Menger Sponges.
Remember this is code-golf the shortest program wins!