Mathematical Knitting

March 3, 2013 at 8:33 pm | Posted in Fiber Art, Knitting | 1 Comment

The folks over at Botanica Mathematica have started an art project that’s right up my alley: illustrating mathematical concepts through needlework. I found them through Ravelry, where there’s a group to coordinate things.

One of the first projects: a knitted binary tree. Having spent too much time during my computer science degree dealing with the things, of course I had to play!

Technically this is a perfect binary tree, since all the levels are completely filled. Of course there could be other versions, where not all branches are present. This would also be nearer to a natural growing tree, since nature tends to be messy. The important part so it stays a binary tree is that at each intersection, the branch splits in two.

Naturally other types of binary trees are knittable as well, but if you want the smallest branches to have always four stitches, calculating how many stitches to cast on and how to split can get a bit more interesting. To illustrate, I drew a few examples:

To the left is the perfect tree, this is the one described in the original instruction. The tree in the middle has three levels on the left side and four on the right. The tree on the right is even more sparse. You can easily calculate the number of stitches starting from the top: The last branch always gets the number “4″. When two branches meet, the branch below gets the sum of the stitches of the branches meeting. Repeat till you’re at the trunk, and you know how many stitches to cast on.

Those concepts are really fun to play with, I’m very tempted to do another one! As if I didn’t have enough projects on the go as is.

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