Adventures in Fibonacci Weaving

This is about the interconnectedness of all things.

FibonacciIn 1202, Leonardo Pisano Fibonacci, an Italian mathematician, wrote a book called Liber abaci (“Book of the abacus”). In this book he posited a problem:

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?

Rabbits?! Squee! Bunnies!

The answer of course is the number sequence for which he is well known, and which bears his name, the Fibonacci sequence, also known as the Fibonacci series:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. Each number in the sequence is the sum of the two preceding numbers.

So what does this have to do with weaving?

Read on, my pretties. Read on.

The sequence describes growth. While it theoretically describes rabbit population growth (actually there are usually 5-8 kits in a litter, so he was off there), it actually does describe the way many other things grow.

sunflower 250w

Especially spirals.

Snail shells. Animal horns. The arrangement of seeds on sunflower heads and many other flowers. The spirals of pinecones. The spirals of rose petals. Pineapples. Leaf nodes on branches. Unfurling ferns. Artichokes. Hurricanes. Galaxies.


Well, that’s really cool. But what does it have to do with weaving?

I’m getting there. Promise.

It turns out that as the numbers get bigger and bigger, they approach what Pythagoras first described as a golden ratio or golden mean. Other bigwig genius types like Johannes Kepler and Leonardo da Vinci were working with the golden ratio too, so it was a big deal. But what is it?

Technically speaking, it’s an irrational number equal to (1 + ?5)/2. In layman’s terms, it’s approximately equal to 1.618.

And this is where it gets interesting.

Proportions of the human body have this ratio all over it. People vary, to be sure, but there are averages. Distance from floor to navel : distance from top of head to navel = ~1.618. Distance from navel to knee : distance from knee to floor = ~1.618.

And you know how you can curl up your fingers? The lengths of your finger segments follow the same ratio from one to the next, just like a snail shell.

Studies have shown that when test subjects unfamiliar with the golden ratio viewed random faces, the ones they judged most attractive most closely matched golden ratio proportions between the width of the face and the width of the eyes, nose, and eyebrows.

The sequence happens in nature so frequently, and in us, that our brains are sort of biologically programmed to find it attractive. It’s instinct.

This is where weaving comes in.

If you’re looking for a sequence of numbers to use for alternating colors of warp threads, and you don’t want to just repeat the same number over and over, if you want something more interesting, but you want something you know will look good, use Fibonacci numbers. Our brains like them.

riin in shawl

So that’s what I did for this shawl, which I wove using five skeins of my Superwash Sport.

I used three skeins for the warp, one skein each of Purplesaurus, Rain Forest, and Coastal (which I labeled A, B, and C, respectively), and two skeins of Cobalt for the weft.*


shawl skeins

Left to right: Purplesaurus, Rain Forest, Coastal, Cobalt (2 skeins)

I already knew I was going to weave this on my Kromski Harp 24″ rigid heddle loom with a 10 dent reed, using the entire 24″ width. So that’s theoretically 240 warp ends. It’s actually 5 holes per inch though, and then each hole has a corresponding slat. It always seems weird to me to have one warp thread on the outside, not through a slat, so I don’t use the end hole that would require using the adjacent slatless slat that isn’t a slat but just wide open space. (Am I the only one who avoids it?) So, 238 warp ends (119 pairs of threads).

I started writing down my Fibonacci sequence, and quickly realized that if I kept on going, I would be using much more of one colorway than the others. For this project I didn’t want to do that (but for another project I might!), so after I reached 21, I started over at 1 again.

So this is what I came up with.

  • Color : # of warp pairs
  • A : 1
  • B : 1
  • C : 2
  • A : 3
  • B : 5
  • C : 8
  • A : 13
  • B : 21
  • C : 1
  • A : 1
  • B : 2
  • C : 3
  • A : 5
  • B : 8
  • C : 13
  • A : 21
  • B : 1
  • C : 1
  • A : 2
  • B : 3
  • C : 4, only because I ran out of room. If I was doing a wider piece, it would be 5.
  • Total: 119

Because I am lazy, I am a great fan of the direct warp method. When the warp is too wide to fit on a warping peg, I improvise.

stool legs as pegs

The two chairs rammed against the table hold the stool the proper distance away from the loom clamped onto the other end of the table. One half the warp wraps around one stool leg, and the other half around the other stool leg, so it’s sort of close to straight-ish.

warp rotated resized

Not bad, eh? Aside from being a really weird photo, I mean.

So this

weaving in progress

became this.

shawl width 600w

Because everything is interconnected.

Want to read more about Fibonacci and the golden ratio? Try here, here, and here.

*My two skeins of Cobalt were from the same dyepot, but I knew there was still the possibility that one could be different enough from the other that it would be obvious where I changed skeins if I used all of one and then all of the other. So I alternated skeins. Every time I ran out of yarn on my shuttle and had to wind more, I wound from the skein I hadn’t just used. That way any major changes were distributed throughout the piece. I would recommend doing the same thing if you run out of yarn on a project and have to introduce a new skein. Alternate for at least a few rows so any change is more gradual.