Do you have a bunch of old business cards that you don’t know what to do with and a chunk of spare time? Then you have the only two ingredients that you need to make a Menger sponge.
So, pay attention and let’s get down to turning those old business cards into a kickass Menger sponge.
No. we’re not talking about the Arsenal manager, that’ll be Arsene Wenger, or those crazy Dutch Eurodance nutters banging on about going to Ibiza. That’ll be the Vengaboys.
What’s that? You don’t have business cards? Grab a load off your dad or your pals who have actually got a job. Your paper round doesn’t qualify as a job that you need business cards for. You should really have tried harder in class.
Just one thing, though. You’re going to need a lot of business cards. Perhaps you can get some printed at one of those machines in a motorway service station. And while you’re at it you may as well form yourself a company.
Anyway, back to the Menger sponge. This baby is a type of fractal. That’s something that has a repeating pattern at every level of scale. It’s seen in snowflakes and can also be used to define the creation of galaxies. Dang, these fractals can be found everywhere, here are just a few things that are made up of fractals:
- River networks
- Fault lines
- Mountain ranges
- Lightning bolts
- The horns of a mountain goat
- Your own heart rate, dude
- Your blood vessels
- Ocean waves
Repeating patterns are everywhere. You just can’t get away from them. Whether you’re out surfing a wave, chowing down on chicken or riding a goat across a mountain range, you’re gonna bang into one.
So, this boffin dude, Karl Menger, came up with the idea of a fractal solid that’s just one big cube. Picture that cube in your tiny mind, yeah?
Now remove a cube in the center of each face and a cube right in the center of the cube. You’re left with a structure consisting of the eight small corner cubes plus twelve small edge cubes holding them together.
Still with me?
Now, keep repeating this process on each of these remaining 20 cubes. Repeat again. And again. Forever.
You’ll either get proper bored or have a really cool Menger sponge. Cheers Menger dude, the results of your big thinking mean we can now ditch some business cards.
So, now it’s your turn. Get those business cards out, place them down on the table and let’s go build us a Menger sponge.
To make a cube out of six business cards, first take two cards and place them across each other at right angles, centering them as nearly as possible. Fold the flaps of the bottom card down over the top card. Turn them over and repeat. Pull the two cards apart. Six of them can be assembled as shown below to make a cube. All flaps have to be on the outside of the finished cube.
When you have two cubes, they can be linked together by taking the two flaps on one face and tucking them under the corners of the two flaps on the adjacent face of the other cube. This makes a pretty sturdy join.
Keep adding cubes together to build up your Menger sponge. Keep going!
Have fun, chumpy. I’d like to hear how you’re getting on, so leave me a comment and let me know how your business card baby keeps on growing.
You is a lightning bolt, an earthquake, you are the ocean waves. Oh, and also a pineapple.