The Fibonacci Sequence in Weaving

I have a near total aversion to math. I have many childhood memories of sitting at the kitchen table doing my math homework with my dad in tears. I was definitely an English Language Arts student who loved to write poetry, and as I became older, gravitated more towards the arts. With this in mind, it’s just a little ironic that I’ve grown to rely on an Italian mathematician to help me in the design of my weaving projects.

Who Exactly is Fibonacci?

Fibonacci was the nickname of Leonardo Pisano who was born in Italy in 1170. He was dubbed the greatest Western mathematician of the Middle Ages and is credited for developing the number system the we use today. Of course, that’s probably his most important contribution to math- imagine if we were all still stuck with the Roman Numeral system. However, what I’m most impressed with is his discovery of what has come to be known as the Fibonacci sequence. The Fibonacci sequence is one the most famous formulas in math. The sequence goes like this: each number in the sequence is the sum of the two numbers that precede it. So, the sequence is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

The Fibonacci sequence has been called “nature’s secret code” or “nature’s universal rule”. That’s because Fibonacci numbers are all around us in nature. Take flowers for example. If you were to count the petals of a flower, it’s highly likely that it’s a Fibonacci number. The flower would have likely have 5, 13, 21, 34 or 55 pedals. Amazing, right?

There is an offshoot of this formula known as “the golden ratio”. There is a specific formula and when plugging in numbers into the formula, if the answer is close to 1.618 the numbers are said to have “the golden ratio”. The great thing is, is when you plug in any Fibonacci sequence numbers into the formula, the answer comes out to be 1.618. Amazing! In geometry, when the Fibonacci sequence is applied as a growth factor, a special spiral forms where the spiral gets larger by a factor of 5 for each quarter turn. This can be seen in nature in such living organisms as seashells, the spiral on a snail’s shell and spider webs.

A bit too mathy? Just know that using the Fibonacci sequence helps us with proportions in our designs. Want to learn a little more?- check out this video on YouTube: What is the Fibonacci Sequence?

Using the Fibonacci Sequence in Weaving Design

I will tell you that I struggled designing my weaving pieces before coming across the Fibonacci sequence. I don’t use the sequence as a hard and fast rule, but it certainly is helpful in giving you a starting point in approaching your designs. Let me show you how I used the Fibonacci sequence to design dishtowels for my friends.

In September I traveled to Maine with a few friends to hike. We stayed near Acadia National Park and climbing (driving actually) to the top Cadillac Mountain to see the sunrise was top on our list. I used the photo I took at sunrise as the inspiration for the towels.

Let’s see how I married the inspiration photo and the Fibonacci Sequence to design the towel. Let’s start with warp.

Here’s the plan for the warp on my iWeaveIt software. Just as a side note, I’m planning on weaving the towels using 8/2 cotton sett at 18 epi in plain weave. As you can see, I used the Fibonacci number “3” to divide my warp. Section 1 correlates with the sky, section 2 the sunrise and section 3 the mountain. I opted to have an asymmetrical design meaning that each section does not take up the same amount of space.

Let’s see how I used the Fibonacci numbers to design the mountain part of the warp. I used the color “brown” as a base color and “sierra” for the stripes. I used the Fibonacci numbers 1, 3, 5, 8, 13 and 21 as pics to create the stripes.

Now for section 2. I divided the sunrise section into Fibonacci number 3. I used the color “yellow orange” as the base color and, for the bottom section, created 5 stripes (3 of which were using “rouille’ and the other 2 “orange”). Remember that I’m using Fibonacci as a guide and not a hard and fast rule?- I chose to only have 2 stripes (not a Fibonacci number) for the top part of the sunrise.

Now for the sky. I used a “gris pale” for the base color, “vieux blue” for 4 of the stripes and “marine” for the remaining 2 stripes. I used Fibonacci numbers to help with the size of the stripes as you can see below as I threw one pic (then base color), 3 pics (then base color), 5 pics and so on.

So that’s the warp, let’s see how I used the Fibonacci numbers to help with the weft. Here’s a picture of the total towel on my iWeaveIt software. As you can see, I divided the towel into Fibonacci number 5 sections.

For the sections where I was attempting to emulate the sunrise and the sky in the warp I again used my new friend Fibonacci. Getting the idea now? Again, you don’t need to get stuck in only using the Fibonacci sequence numbers in your designs. It’s certainly a very helpful starting point especially if you’re getting a little stuck in the design process.

With all the color changes the towels took a little bit of time to weave. Here’s a picture of one of the finished towels. If only colors came out correctly in the photo- they look so dullish in the picture, but actually the browns are really deep and the oranges and yellows are vibrant. They are actually really soft and pretty and I think my friends will see the sunrise right away.

Good ole’ Fibonacci. He really helped me with this project. If you haven’t yet, consider trying the Fibonacci sequence in your designs.

2 Comments

  1. Susan Wright
    January 18, 2024 / 2:49 am

    Hi – I am the Program Coordinator for my weaving guild which is based in Massachusetts. Our members have requested a program on Fibonacci sequence and designing. Would you be interested in doing a zoom program for our guild for our 2024-2025 program year which starts in September 2024? If so, please let me know so we can discuss what your fee might be and your availability on a Saturday either at 10:30 a.m. or 1:00 p.m. We are looking for a 60-90 minute program on zoom.

    Thanks so much!

    • March 25, 2024 / 3:10 pm

      Hi Susan. Thank you for considering me, but I feel like I’m just too new of a weaver to do something like this. You may want to reach out to Jane Stafford (Jane Stafford’s online weaving guild) as her video on division of space was very helpful and incorporates the Fibonacci Sequence.

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