Flying through a 3D fractal

A Menger sponge is created by starting with a cube a recursively removing chunks of it. Draw a 3×3 grid on one face of the cube, then remove the middle square, all the way through the cube. Then do the same for each of the eight remaining squares. Repeat this process over and over, and do it for each face.

The holes are all rectangular, so it’s surprising that the geometry is so varied when you slice open a Menger sponge. For example, when you cut it on the diagonal, you can see stars! (I wrote about this here.)

I mentioned this blog post to a friend at Go 3D Now, a company that does 3D scanning and animation, and he created the video below. The video starts out by taking you through the sponge, then at about the half way part the sponge splits apart.

2 thoughts on “Flying through a 3D fractal

  1. Visualisations of this type make the Menger sponge look fairly solid.

    Remember, the limit object has zero volume! As you continue to iterate, it looks more like a very fine mesh, and then disappears to nothing.

  2. Sure, this is something related but different, and in some ways more interesting: an early stop along the sequence leading to the Menger sponge.

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