### Algebraic Expressions of Handwoven Textiles

by Lana Schneider

For me, the study of Algebraic Expressions of Handwoven Textiles by Ada K. Dietz began in 1989. One of my earliest weaving friends, Louise Schmidt from Riverside, CA, offered to present it as a guild program..."but I am 84, so I had better teach it to you, in case I don't feel well." Louise had taken a workshop with the Riverside Weavers Guild around 1970 at Ada's retirement home in Yukaipa, CA, and really enjoyed the experience. But time had distanced anyone's awareness of its existence. With Louise, I spent a delightful summer trying out the formulas in a number of weave structures. It went into my catalogue of creative resources and appeared intermittently amongst my projects. In 1997, when Handwoven called for weavers to describe how they worked with stripes and plaids, I thought it an opportunity to draw others into the process. I reworked samples, sought words that would explain the concept simply and intriguingly; I was again caught up in the pleasure of this concept. The result was the article, 'Designing Algebraically', included in the Jan/Feb 1998 issue.

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The little niche of history that captures Ada Dietz' work is significant as well. It is an opportunity to drop back a few decades and connect with weavers whose enthusiasm and creativity mirrors our own. As a weaving student in 1946, Ada was encouraged to create original work rather than simply follow established patterns. She logically fell back onto her career in mathematics. She and Ruth Foster began to see where the idea would lead them, which ultimately was to Louisville, KY.

Ada submitted a hanging woven in summer and winter with the formula *(a+b+c+d+e+f) ^{2}* to the Country Fair held at the Little Loomhouse. The response to this piece was so remarkable that Lou Tate, founder of The Little Loomhouse, invited the two weavers to conduct a summer-long study for her experimental weaving group.

The booklet, *Algebraic Expressions in Handwoven Textiles* arose out of that collaboration. A travelling exhibit was also developed which, during the fifties, the two women took to weavers throughout the United States, sharing the concept of designing by formula. Two articles that chronicle the development of the use of algebraic expressions were published in *Handweaver and Craftsman Magazine* indicating the enthusiasm with which it was received at the time. They were published in Spring, 1953 and Summer, 1959.

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The work of Lou Tate at her Little Loomhouse in Louisville,KY, was virtually unknown to me, except as the publisher of the *Algebraic* booklet. My opportunity to visit the historical weaving school and meet with the people that had worked with Lou Tate, with those involved in preserving this significant portion of our weaving heritage, brought a new connection to this study for me. Lou Tate was trained at Berea College, Berea Kentucky, and spent her early years travelling throughout the Kentucky Hills, documenting and collecting original handwoven coverlets. She was a strong force in weaving in the Kentucky-Indiana area for four decades. A young contemporary of Margaret Bergman, of Poulsbo, WA, the two worked together annually until World War II made the journey no longer possible. I have heard of what great respect Mrs. Bergman generated here in the Northwest since my move here in 1992. It was a surprising connection, but one that pleases me greatly. It highlights the opportunity weavers have always had to support each other in their personal work, to their mutual enrichment and to the furthering of the craft of weaving. Information on the Little Loomhouse and its ongoing work as a museum and weaving school is available from:

- Lou Tate Foundation
- P.O. Box 9124
- Louisville, KY
- 40209-0124.

Basically the idea Ada Dietz developed is to create an algebraic equation, giving a value to each element you wish to utilize in a specific textile. Two colors would be a simple formula *(a + b)*. You then decide on a degree of complexity with which you want these chosen elements to interact -- 2 or 3 being the more common choices. Expanding the formula to its simplest level, you establish the order in which an element is used. For example, *(a + b) ^{2}*

multiply the phrase by itself

(a + b)(a + b)multiply the individual elements in the first parentheses by all the elements in the second parentheses a(a + b) and

b(a + b)which becomes a^{2}+ ab + ab + b^{2}which breaks down to aa abab bb

You would then substitute a color or texture or a block weave structure for the *a*'s and *b*'s in the order presented. To add elements, you increase the number of unknowns, such as *a + b + c + d*, etc. To increase the interaction of elements you increase the multiple power, which means you continue to multiply a simple parenthetical phrase with the previously multiplied power. You can have a grand time driving yourself crazy! I have woven up to four elements multiplied by the fourth power and eight elements squared, which created a Christmas wall hanging. See *Handweavers & Craftsman*, Spring 1953 for the picture of this premier piece of Miss Dietz' work.

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I am glad to have found this quirky design tool, and I appreciate the heritage of weaving history that I connect with in the course of its study. However, weavers frequently express to me their "math phobia" and rather too quickly dismiss the potential this study might hold for them.

The formulas merely offer a focus for design possibilities; higher math skills are not a prerequisite. I needed to "explain" the formulas so they made sense to me. But, just as with any other pre-set pattern, they can be used as presented in the study booklet Miss Dietz developed without calculations, and adapted to the textile by substituting a chosen yarn or weave structure. The results are remarkably versatile. By varying the yarn, the weave structure and how the repeat is handled, you create endless variations, but all contain a pleasing proportion and transition of elements.

This study also extends an excellent example of the value of block profiles. Particularly in the more complex formulas, the threadings and treadlings are presented much more clearly when considered in pattern repeats, that is, blocks, than when written thread by thread in weaving graphs. A weaver can quickly grasp the concept of substitution when she sees how many varied textiles are achieved with the same formula.

I never seem to come to the end of this study. I started using the simplest formula in as many structures as I could think of; I have used one structure -a twill study- in an ever increasing complexity. This time I was going to methodically work my way through the booklet written by Ada K. Dietz as it was developed for study groups. As I already had so much background work accomplished, this seemed like something readily achievable. What I accomplished was to accumulate a growing list of questions, with preliminary, but by no means definitive evaluations. I find there is still more to learn here and list a few :

##### What effect would different treatments of the repeats accomplish?

The simple observation is that there are two ways repeat a pattern: progressive, that is from point *a* to point *b*, *a* to *b*, *a* to *b*... and mirror image, which would reflect *a* to *b* to *a* to *b*...It is with the mirror image that the possibilities multiply. In fact, there were so many possibilities to explore, I simply had to stop trying in order to continue with the study. This was more apparent in the simpler formulas. It is just easier to play with variations on reversing an 8 block profile of (*a + b*)^{2} than it is to keep track of other than the most logical repeats of (*a + b + c + d*)^{2}, with its 32 block profile. One of the effects of manipulating the reverses is to generate more interesting interaction between the design elements. The more complex formulas are interesting enough as they are formulated. I did find that on some of her larger pieces, Miss Dietz did not start at the beginning and continue through to the finish of the extended formula. Often she began at the last segment, then went into the full formula, attending to border designs as she did so. This is certainly one area where more experimentation can be conducted.

##### What about using different yarn combinations, different, sett, different finishes?

Where possible, I used yarns similar to those mentioned in the study. I thought it would be difficult to enjoy the combinations popular in the 40s and 50s, but this was not often the case. I achieved some pleasing effects with a versatile combination of yarns not commonly used in today's weaving. Rarely did Miss Dietz use the same weft as the warp for her background yarn. More frequently, she used yarn that contrasted with the pattern yarn, often with added texture in a very fine thread. The added color supported the pattern while balancing its impact in the overall cloth. You see this to great design impact where she combines a twill treadling with plainweave. The tabby not only adds balance in tone, it supports the cloth in a way twill treadling alone does not.

##### What effects are possible with block treadling variations?

As a basis for my study, the main sample was woven as drawn in. I often experimented with alternate treadlings, such as twill on overshot, color and weave, even weaving only one block repeatedly. The effects were very pleasant. It occurred to me that the more complex formulas offer a wealth of potential combinations of blocks, quite unlike the formula sequence, and yet another source for further exploration.

What I have achieved is enough to create a number of textile projects with the information already acquired. What can be achieved will remain for continued study. I would be glad to support anyone's further effort in experimenting with this study. Contact Lana Schneider with your questions.

For those of you who want to see where this study leads yourselves, I suggest starting most simply.any formula can be pleasantly demonstrated in plainweave with colored or textured yarns substituting for the variables in the formulas. Used simply as a border repeat, the threading is easily and effectively presented. For more complex cloth, more complex substitutions are called for, and variety abounds with treadling variations. A group study approach can follow several paths: select one formula and weave any number of weave structures, include the exploration of treadling variations, select one formula and explore various repeat possibilities using the same yarn and weave structure, weave the same basic formula in increasingly higher multiplication to observe the complexity of interaction.

Lana Schneider began weaving in 1986 at the Tri-Community Adult Education class taught by Janice Martens. "It was a marvelous opportunity to totally immerse myself in the diversity of weaving. Moving to the NW in 1992, I began working on my COE in Spinning, attaining the technical level at the 1993 judging. My commitment to continuing to pursue the challenges of this textile world as I assume the role of president of the Seattle Weavers Guild in 1999-2000."

The Olympia (Washington) Guild established a scholarship in memory of an influential weaving teacher from Evergreen State University, Hazel Pattison. The Hazel Pattison Memorial Grant provides a monetary support for a year-long personal study. The Algebraic Expressions study was underwritten by this grant. While all of the recipients are responsible for presenting their work in a guild program format, several have also resulted in study notebooks that will be maintained in the library for the benefit of future guild members.

The original samples of Ada K. Dietz and Ruth Foster and further study materials are available thru the HGA Textile Kit: Algebraic Expressions in Handwoven Textiles. It is a great reference, with Eileen Hallman's documentation and study sheet.

*Copyright © 1998 by Lana Schneider. Please contact the author for permission to use any part of this article*.