Menger sponge video

Posted on November 10, 2007 by Brent

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:

  1. Start with a solid cube.
  2. Slice the cube into 27 equal little cubes, by making two parallel slices in each dimension (just like a Rubik’s cube).
  3. 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.
  4. 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.

About Brent

Associate Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
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6 Responses to Menger sponge video

  1. Steve Gilberg says:
    November 13, 2007 at 10:05 am

    Whew, what an unusually rapid series of posts you made.

    Zero volume and infinite surface area aren’t so incredible when you realize that the same applies to a plane.

  2. Brent says:
    November 13, 2007 at 11:17 am

    It’s because I should be working on grad school applications and I’m procrastinating. =)

  3. David Makin says:
    November 17, 2007 at 8:16 pm

    Thanks for featuring my video – apologies for the quality but there’s not much I can do about how YouTube treat uploads.

    You may like to see these:

    http://makinmagic.deviantart.com/art/Menger-Homes-2-69784548
    http://makinmagic.deviantart.com/art/Menger-Slices-69482789
    http://makinmagic.deviantart.com/art/Lego-69038435

    All created using my 3D IFS formula for Ultrafractal which can be found in the mmf4.ufm in the Ultrafractal formula database here:

    http://formulas.ultrafractal.com/

  4. Brent says:
    November 18, 2007 at 5:27 pm

    David: I’m glad you commented, since I always like to give proper attribution but didn’t really know who had made the video. And thanks for the links, that’s some cool stuff. =)

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