###### Posted by Peg in South Carolina

WARNING.:This is very much an in-my-head theoretical post. Read at risk of extreme boredom

Earlier I had focused on the threading I would use for this shawl. Go to this post to read about that. Later I went on to consider the number of blocks and their order. Go to this post to read about that. So for now, I have come up with the number of blocks and the width of the blocks. I also have the order of the blocks. This is the order.

A B C D E F G F G F E D C B A

These count out to be only 15 blocks. I have not, however, extended it to encompass the full width of the shawl, i.e., 44 blocks. And I’m not quite ready to do yet. What I want to ponder for awhile are the motifs.

One thing I know is that the shawl will be a much larger canvas than this small sample. Consequently the motifs will have to be designed to fit that larger scale. But I have not figured out how that will happen.

I have worked out four different motifs, based on what I see in that sample I have been using as the basis for my designing. Each motif consists 3 groups of blocks, 2 identical to each other and surrounding the different one in the middle. There are four of these.

Right now these motifs are only rough sketches in my mind. The photo to the left shows the ideas I began with and from which I developed (in my head) the four motifs. For now, however, the development out of this germ into four individual motifs is going to stay in my head. I need to have the exact order of the blocks across the whole weft. And I need to decide how long the units of each motif are going to be and how long each motif, with its units, is going to be. But all of these are inter-related and as one develops, that development may change the development of the motifs themselves.

What I am thinking about now is how to order the motifs along the length of the piece.

My first thought was to order them in what seemed the best order, decide how much red (and shadow blue) to weave between them, and weave a strictly ordered shawl. Perhaps reversing the sequence for some variety.

But as is my wont, my thoughts have started getting more complex. I retrieved Ada Dietz’ monograph called *Algebraic Expressions in Handwoven Textiles*. She uses various polynomials raised to various powers for her designing purposes. Because there are four motifs, I decided that the most workable polynomial to use was (a + b + c + d) raised to the 2nd power. On page 30 Dietz translates this into the following written-out form:

aaa babacacadad bbb cbcbdbd ccc dc ddd

I have read somewhere (?) that mathematically this is incorrect. But I am concerned about design, not mathematics. So what this means is that I would repeat motif 3 three times, then alternate motifs b and a then c and a and then d and a, then repeat the second motif three times, and so on. If I wanted, I could balance this out by returning from the end back to the beginning.

Of course I will still have to decide which motif to associate with a, which with b, and so forth.

Why would I rather do something like this instead of a very simple ordering? Because I love the appearance of randomness undergirded by order. This is why mathematical approaches fascinate me.

But before I can move forward, I need to go back to the ordering of the blocks and the effect of that ordering on the four motifs. Here is how I have expressed it on my crackle shawl to-do list:

Work out the ordering of the blocks for the crackle shawl, after which (or during which) I can contemplate the effect that order on the appearance of the four motifs

This will NOT happen tomorrow!

For those who have just come to this blog, and for those readers whose memories are faint (!), here is a picture of the end-of-another-crackle-warp sampling that started this whole shawl business. My original intention, after finishing this sampling, was to develop the part visible to the left at the top. But after this sampler had hung on my door for a few days, I realized, no, the part to the right at the top is what I wanted to develop.

**Related Post:**

Binary Sequences and Designing

Resisting Doing the Work

"Crackle Shawl—The Motifs” was written by Margaret Carpenter for Talking about Weaving and was originally posted on February 10, 2009. ©2009 Margaret Carpenter aka Peg in South Carolina

## 2 comments:

I know it's not the point, but the bit about the equation niggled me so I tried it out.

The original equation multiplies out to:

a squared + 2ab + 2ac + 2ad + b squared + 2bc + 2bd + c squared + 2cd + d squared

which could reasonably be interpreted as

aa abab acac adad bb bcbc bdbd cc cdcd dd

change the spacing and that's what you had.

Not that it matters :)

Thank you for sharing your work!

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