Botanica Mathematica

a textile taxonomy of mathematical plant forms


Binary Bonsai

Simple Binary Tree

simple binary tree in Misty Alpaca chunky yarn on 6.5mm dpns.

These little trees are knitted in the round and repeatedly divided in two to form branches and twigs. They could also be crocheted but I haven’t tried it yet so I’ll talk in terms of knitting. Once I get time to try it I’ll write it up. In the meantime have a go yourself once you get the idea of the knitting.

The choice of yarn and needles is up to you. Browns and greens are best for colour. Thickness of wool and size of needles can vary but it’s best to work to a slightly tighter tension so the stuffing doesn’t show through. I’ve used a set of five double pointed needles in my test pieces but you could use circular needles and the magic loop technique. Spare dpns are handy as stitch holders towards the end and when you’re making i-cord branches.

In order to be successful with all these divisions you need to start with a power of two stitches. Not just a multiple of two – every time you divide your stitches in two each part must also be divisible by two. So you need numbers like 4 (2×2) or 8 (2x2x2) or 16 (2x2x2x2) or 32 (2x2x2x2x2) and so on. The first couple of these will give you a very small structures without much branching so I’d recommend starting with 16, 32 or 64 stitches, depending on the yarn and needles chosen.

Once you’ve decided how many to start with cast them on, join in a circle, place a marker at the start of the round and knit the trunk of your tree. Trees come in many shapes and sizes so you can make it short and squat or longer and thin. For your first tree I’d knit as many rounds as you have stitches cast on.

Now place half the stitches on a holder and knit rounds with the rest. Your first branch is under way. As many rounds as you have stitches and then split again. Keep doing this until you run out of stitches. Cast off and break the yarn.

Rejoin the yarn at the smallest split pick up the stitches and work to the end. Then go back and to the next smallest split and work to the end splitting as you go. Eventually you’ll work back to the first split in the trunk and so you pick up the stitches and work the same branching structure at this side of the trunk. Once you’ve run out of stitches to pick up and all the branches have tapered off then stuff the tree with toy stuffing. Gently push the stuffing into the branches and the floppy tree skin you knitted should start to support itself.

When you are a happy that the tree is well stuffed stitch a piece of felt across the bottom of the trunk or pick up stitches round the hem and knit a base – if you want you could even knit a few big roots to make it more realistic.

If you’d like to contribute your tree to the Botanica Mathematica specimen collection please send it, with a note of your name and location (and anything else about it you think we’d find interesting), to:

Madeleine Shepherd
Coburg House Art Studios
15 Coburg Street
United Kingdom

Simple Binary Bonsai Pattern

  1. Cast on 16 stitches, join in a circle, place marker.
  2. Knit 16 rounds.
  3. Place 8 stitches on holder.
  4. Knit 8 rounds on remaining 8 stitches.
  5. Place 4 stitches on another holder.
  6. Knit 4 rounds on remaining 4 stitches.
  7. Place 2 stitches on another holder.
  8. Knit 2 rounds on remaining 2 stitches.
  9. Cast off and cut yarn.
  10. Pick up 2 stitches from line 7, rejoin yarn and work lines 8 and 9.
  11. Pick up 4 stitches from line 5, rejoin yarn and work lines 6 to 10.
  12. Pick up 8 stitches from line 3, rejoin yarn and work lines 4 to 11.
  13. Tuck all the ends of yarn inside the tree. if there are any odd gaps stitch them closed with some spare yarn.
  14. Stuff tree with toy stuffing.
  15. Close the base of the trunk with knitting or by stitching a circle of felt in place.

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The Language of Nature

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.
Richard Feynmann in The Character of Physical Law

Botanica Mathematica is our attempt to express one dialect of this language in an visual and tactile form.

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On Growth and Form in Nature

That’s the journal called Nature, actually.  There’s a nice piece on D’Arcy Wentworth Thompson’s great work on mathematical biology On Growth and Form in the current issue.

On Growth and Form was one of the texts I referred to when this project was taking shape.  There’s very little botany in the shorter, popular edition I have – mostly zoological examples – but it inspired me to look at the modern developments (of which I’ll say more in a later post).  Botanica Mathematica is the result of my thinking and making with this in mind.  If you want to know more about this maverick zoologist/classicist/mathematician here’ a good biography and a lovely picture of Thompson and his parrot at an ice cream shop in St Andrews!  you might also want to check out the art exhibitions in the University of Dundee .