Menger Sponge

The Menger Sponge is the three-dimensional analogue of the Sierpinski Carpet. Start with a cube, divide it into 3 x 3 x 3 smaller cubes, and remove the center cube together with the six cubes in the middle of each face. Then repeat that same rule on every cube that remains.

That means 20 cubes survive at every step, so the shape becomes much denser than the 3D Vicsek Fractal, which keeps only seven cubes, and more regular than the Mosely Snowflake, which uses slightly different cube-removal rules. Even so, all three belong to the same recursive voxel family.

One of the most surprising facts about the Menger Sponge is that its volume tends to 0 while its surface area grows without bound. That makes it a perfect example of how fractals can look like solid objects and still behave in very counterintuitive ways once the recursion continues indefinitely.