Sunday, March 17, 2013

Designing with Farey Fractions

This post may be a bit premature because I haven't yet woven off my Farey Fraction designs on this towel warp.  Who knows if the designs will meet my expectations or not.

The journey started with needing to do a paper for the Computer Aided Design Exchange for Complex Weavers.  I did the paper, had some errors that needed fixing and then got into a nervous nelly fit about whether or not my designs would actually weave into anything that looked like the vision I had in my head.  I don't know about you, but once I start doubting myself, it can be hard to go forward.  I kept the paper on a back burner and decided to weave some of my ideas on a towel warp which would either prove the design value or let me know that it was just a gimmick.

The paper is based on Farey Fraction denominator sequences used in weaving design.  That's a mouthful, isn't it, but not nearly as intimidating  in practice as it sounds.  Ralph Griswold wrote a paper about designing with the sequences  and you can find his work here.   I learned about the sequence and its design possibilities from a FaceBook post by Marg Coe, so I'm not working with brand new ideas, just trying to expand them with my own touch.

I found an online calculator to make the math part easy for me.  From there, I just used the denominators as a threading sequence and experimented with various tie ups and treadling sequences.  My idea was to have a complicated threading that could be woven with a simple treadling sequence on my Baby Wolf.  When I got right down to warping the loom, however, I decided that I would put in on the AVL, add a basketweave selvedge and treadling my threading to avoid threading errors.  To top off the complications, I saw a natural color sequence in my draft and it was awkward  because I used a sett of 20 epi and my color sequence was 12 red and 11 navy, which made every bout I wound had to be calculated for color.

Let's get down to a sample draft.  Start with a denominator sequence based on the number 8.  Here is the threading.

I then advanced the threading one step seven times. (This creates a threading that comes back to the original threading after the seven advances. What you see below is only a portion of the threading sequence and is still in the 8 shaft form before selvedges were added.   I have done 12 different tie ups and a variety of treadling sequences for my 12 yard towel warp.  Once they are off the loom, tell me if you think they they were worth the fuss!
What I like about this design is how the pattern changes in each red warp section - sort of like looking through a fence.  Some of the drafts are better with a light colored weft which shows off the design in the wine colored warp.
And, no, I don't mind if you use this draft or expand on it for your own use.  I really think it would make a good draft for a weaving demonstration - change your tie up and you get an entirely new design peeking at you through the fence.


  1. This is a very cool concept, and I like the resulting draft, but I have one observation. Since you are striping, the lighter stripe shows an offset pattern which bothers me, it seems to need one more thread. What if you think of the light stripe as A, and the dark stripe as B? Doing this, you will have a balanced point twill for A, and the unusual Farey Fraction for B, and each one can be advanced: A B A' B' A'' B" etc.

    1. Thanks for your comment, Jennifer. You have a great point. Feel free to use the draft and use your own interpretation on it!