Using mathematics to design weaving profiles or sequences is a theme that I return to over and over. I have relied on writings about this subject because my mathematical knowledge is relatively rudimentary. I was very lucky to have found this document in the Ralph Griswold collection of weaving documents stored at the University of Arizona website. "Algebraic Expression in Handwoven Textiles" by Ada K. Dietz

This is my journey into designing a profile and weaving drafts based on the mathematical expression of the cube of a binomial (a + b) ³ My interpretation of this expression is aaa + aabaabaab + abbabbabb + bbb. I regrouped this into aaaaa b aa b aa b a bb a bb a bbbbb Below is the two block profile created from my interpretation.

The next steps are to convert this into weaving draft using block substitution. With four thread blocks, the draft uses 8 shafts. With 5 thread blocks, the draft uses 10 shafts - and so forth. The most common substitutions are with 3/1 and 1/3 twill blocks, but I’ve found that more interesting designs can be had

when you think outside the box. The following draft interprets the profile using 3/1 and 1/3
twills. But this tie up could be altered in one or two quadrants to a
broken, 4 thread twill. What fun that might be.

This conversion uses a regular 5 thread satin and an altered satin tie up

The following draft uses two altered 5 thread twill blocks. I discovered this option in Handweaving.net. To me, the lines look wavey. The surprise is that my weaving software (WeavePoint) analyzed the threading and found it could be woven on 8 shafts. In checking further, I also found that Handweaving.net will compact this draft to 8 shafts as well. How great is that!

Below Block A uses an altered satin tie up and Block B uses a 5 thread altered twill tie up. Busy, but the profile is still visible.

The next draft uses 5 thread satin blocks. The dark block is flipped horizontally and reversed so that dark now becomes light. The draft doesn’t have clean cut edges where the two blocks meet.

There are, of course, many more options to interpret this profile. Feel free to experiment and enjoy the results!