Check out the following totally sweet video of zooming into a Menger sponge!
This video was made by David Makin, who has lots of other cool images and videos at his website. You can probably figure out what a Menger sponge is just from watching the video, but it’s a fractal object which is very easy to make. Here’s what you do:
- Start with a solid cube.
- Slice the cube into 27 equal little cubes, by making two parallel slices in each dimension (just like a Rubik’s cube).
- Remove the cube in the very center, and the six cubes in the center of each face of the big cube. You’ll be left with a cube-shaped object with square holes going straight through the middle on each side.
- Repeat this procedure on each of the 20 remaining little cubes, and so on recursively forever.
The Wikipedia page has some nice pictures that should make this pretty clear if it’s not already. In case the video didn’t blow your mind enough, you should note that Menger sponges have zero volume but infinite surface area! (“How is that possible?!” I hear you cry in dismay. Well, infinity plays very weird games with your intuition!)
Found via God Plays Dice.