Woolhelmina > notebook > projects > Menger Sponge - without the sponge

Project info
Menger Sponge - without the sponge
Knitting
Needles & yarn
Notes

It has taken me a very long time to make this. It is called a Menger Sponge and is a 3D fractal. It is like a Sierpinski Carpet but in three dimensions. It is named after Karl Menger.

My original plan was to make a knitted version and pad it with sponge but all attempts failed.

A year ago we were involved with the Mega Menger project, which used business card-size, pieces to make small cubes which were joined together to make various levels of sponge. If you want to know the details go to the web site where you will find information from round the world.

The basic idea is that you take a cube and remove a square tunnel from the centre, in all three directions; then you remove a square tunnel, in all directions, from the cubes you have left. Theoretically you can keep on doing this to infinity. The volume gets increasingly small; the surface area gets increasingly large.

Ever since Mega Menger I have been turning over the idea of trying to knit a small version. The finished thing looks simple, symmetrical and logical. However I approached it, it proved to be far too complex to attempt to knit. I wanted to make it about the same size as the version I finally made. I could have done this by making lots of 2 cm cubes and stitching them together but I didn’t really want to do that. I wanted to make at least the second size of cube or possibly the big cube all in one go.

Trying to work out the logic of knitting the net, and leaving gaps to put sponges inside, was mind-blowing. After many attempts I gave up and decided to use plastic canvas instead. I thought that, once I had handled the structure sufficiently, I might be able to return to the knitted version. For various reasons, the plastic canvas version proved almost as challenging. I could not make a complete face in one piece because of the complications of what happened on the inside. There are 20 cubes in the finished sponge and each of those has a cross-shaped piece inside to form the smallest holes. Trying to build up a shape that is based on holes is not easy. Joining the cubes together is also tricky when some parts need to be joined inside.

One advantage of plastic canvas was that it was easy to use different colours on different faces. The colours effectively show where the various holes are.

I think I could make a better attempt at a knitted version now but this has taken so long I feel inclined to leave it at this point.

There are 120 6 cm squares and 480 2 cm squares and the whole thing is much heavier than you might imagine.

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Finished
June 28 2015
September 3 2015
About this pattern
Personal pattern (not in Ravelry)
  • Project created: September 5, 2015
  • Finished: September 5, 2015
  • Updated: November 11, 2015