I was trying to do a new post every couple of weeks but I blinked and seven went by at high speed. Part of the whooshing sound they made on the way past included finishing off some stuff, putting off other stuff, making some random stuff out of the ordinary completely on a whim and a birthday with a rainbow cake (what else would she have?!)

The practice cake was less correct colours and had more interesting decoration (Tiny decorated that one herself) and the official one was only hampered slightly by the whole of the Shire (well the bits of it I looked in) suddenly not stocking food colouring anymore in between the time when I bought the stuff for the first one, used twice as much as I thought I would need and then went to look for more. I resorted to eBay and it turned out ok in the end. By the way, in case you were wondering, yes, my choice of where to live was entirely based on the name of the area with no consideration of the suitability and yes, it was just so that I could pretend to be a Hobbit for two years. Don’t tell the Man in the Shed, I don’t think he has noticed yet.

Here is the secret thing I was making for her, it matches the blanket pattern but has different colours. It’s a bit huge but she really likes it and it is in her rocking chair now.

The finished thing is the grey cardigan with the pockets. I have worn it quite a lot (about six and a half weeks worth) already although it is starting to get colder now (note the woolly socks) so I might not wear it so much for a while. I added in some lace ribbing round the bottom, partly because I was convinced the thing was going to roll up all the time and partly to make it a bit longer because I wasn’t sure about the length and it has turned out about right. I am really pleased with it although I think I would do the next size up another time. Mental note: don’t eat all the biscuits.

The random thing was that I saw a dream-catcher with a tree on it when I was looking for some craft to do with the Joeys and it got me thinking about Fibonacci numbers again so I started collecting some bits and pieces together while I thought about how to make it work.

If you don’t know about the Fibonacci sequence then The Rabbit Problem by Emily Gravett is a very good place to start. The short version is you start with two ones and add the two previous numbers together to get the next one – 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. I started to wonder whether you could make a tree that has a trunk with 55 strings that splits into two branches, one with 34 strings in and one with 21 strings in and then carries on splitting all the branches into smaller Fibonacci numbers until you get down to 55 branches that are all made of a single string. I did some scribbling. I thought I took a picture of my notes somewhere but they’ve been tidied up or recycled or something. There were a lot of notes though. And some circular graph paper.

And then I thought to do some research (if you count believing random things you read on the internet without checking them) and it turns out that real trees already had the same sort of idea. I love how much maths there is in nature, it’s almost as if someone made it that way on purpose… Some trees show the Fibonacci sequence in the number of branches that they have at any given point – suppose that when a tree puts out a new branch, that branch has to grow two months before it is strong enough to support a new branch itself. In  the first month you will have 1 branch, at the end of the second month that branch will split and you will have 2 branches, the new branch has to grow for a bit so the next month the original branch will split again but the new branch will not – 3 branches, the next month the first and second branch will split but not the newest one – 5 branches etc.

My tree has the sequence in the thickness of the branches going from the top down to the trunk and in the number of branches going up from the trunk out to the twigs. I’d be interested to see whether real plants follow some kind of tree equivalent of Kirchhoff’s Law (what goes in must come out) in terms of maybe the cross-sectional area of a given branch being equal to the sum of the cross-sectional area of that branch at a thinner point higher up plus any new branches that it has sprouted on the way but I suspect it might be a lot more difficult to measure.

I put one bead on each string (carefully planned for which size to put where, there were a lot of notes, remember?) and arranged them so that one bead is on each branch (except the single thickness ones) and also discovered that rather satisfyingly there are 21 branches with a thickness of 2 strings, 13 branches with a thickness of 3, 8 with a thickness of 5, 5 with a thickness of 8, 3 with a thickness of 13, 2 with a thickness of 21, 1 with a thickness of 34 and 1 with a thickness of 55.

If you are clever you might have noticed that that only makes 54 so there is one bead over which would be carried on to the next branch if my 55 thick branch were going to join into an 89 thick one.

I put the last bead down in the roots to look like a seed that this strange tree might have grown from. The roots are less orderly, I suppose I should have done the sequence going the opposite direction if I had been thinking about it properly but I didn’t. Also I definitely wasn’t trying to get it roughly symmetrical, that pleasing wonkiness is definitely a deliberate attempt to make it look more like a real tree. Definitely.