16/Jan/2006 – Menger’s Sponge   15 comments

Menger’s What Now?

Sponge. Menger’s Sponge.

Photo of a depth 1 Menger's Sponge made out of business cards.

Completed depth 1 Menger’s Sponge made out of folded business cards. No glue, tape, or fasteners of any type, except the folded cards themselves.

Used 192 business cards: 20 cubes of 6 cards each (120,) plus 72 facing cards.

Make your own.

Karl Menger (1902 – 1985) was an Austrian mathematician. He is credited with the first description of a fractal solid called, conveniently, Menger’s Sponge.

I made a depth 1 version (pictured left) out of folded business cards. I am in the midst of constructing a depth 2 sponge. None of this is an original idea, at least, not my original idea. Dr. Jeannine Mosely undertook the construction of a depth 3 Menger’s sponge, but I don’t know if she ever was successful.

Geeky? You bet.

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Posted Monday, January 16, 2006 by Grant in Random

15 responses to “16/Jan/2006 – Menger’s Sponge

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  1. Saw some geekily interesting stuff on PBS the other week.. Mandlebrot Set – very cool images – here are a few sites: http://library.thinkquest.org/26242/full/types/ch6.html

    http://galifrey.triode.net.au/galifrey/Maths/Mandelbrot/mandel.shtml

    have fun*grins*

    "Єpiѕtling ŊutΩpian"
  2. Cool! A use for my boxes full of old business cards. I *knew* I was saving them for a reason.

  3. Love it. I, too, just happen to have a few boxes with old business cards some where in the garage. Hmmmmmmm… That gives me an idea: My nieces and nephews are always creating works of art when they visit. I’m going to have them draw on the backsides of the old cards, and then we will make a patchwork sponge. Artsy meets geeky–I like it!

  4. Well I don’t have any business cards but I do admire the creativity of the thing!

  5. Grant this is so kewl !
    I don’t have old cards but I can use my company ones yeah yeah and use it as art in the lobby……LOVE it !! Be sure to let us know what happens with the new one your doing….
    MAUH

  6. Ooh no, not geek, just an artsy bitsy one 😉 This is almost like Japanase origami Grant. Will look forward to your next level of construction.

  7. Creative!!
    Nice one Grant!

  8. @ Oops: Thanks for the links. I love when left (brain) meets right. Math meets art.

    @ Geek: I’m kicking myself that I had just thrown out some old cards… Ugh!

    @ Tracy H: Glad you liked it… the patchwork sponge is a fantastic idea.

    @ Red: I love the creative aspect of it, too.

    @ Ladydi007: The depth 2 sponge will take a while… I have to collect enough cards, too.

    @ Maayan: Yes, it is very much like origami, which I also love.

    @ Diwakar: Thanks.

    — Grant

  9. lol, I’ve never seen origami quite like this. Have you ever heard of kiragami?

  10. WAY COOL. i was looking for a hobby that would take me years of distraction lol .. keep me up-posted, love this kinda thing

    Cheers for 2006 xx

  11. @ Melissa: I hadn’t heard of kiragami, so I “googled” it. It seems to be like origami but allows cutting of the paper.

    @ modestjaws: Thanks… I’ll post on the progress of the depth 2 sponge.

    — Grant

  12. Quite interesting! My late husband had a master degree in mathematics and science, he would have enjoyed this very much. Thanks for showing, I have to show this to our daughter and son. 😀

  13. Cool photo, I looked at the others in your photo stream. Very creative.

  14. Yeah it’s pretty cool. (Kiragami that is.) I do a meger amount of origami, but have always wanted to try kiragami.

  15. @ Joy: I’m not a math geek, so I cannot pretend to understand the details, but I appreciate the beauty in the results of the math.

    @ Jess W: Thank you.

    @ Melissa: Origami is another of my favorite elements of Japanese culture.

    — Grant

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