BINARY SEQUENCES AND DESIGNING

Posted by Peg in South Carolina

I am definitely mathematically challenged so that I should be using the above words in a blog title is nutty.  How did such a thing happen to someone who has trouble adding 7 and 13?

I found a blog. Nigel’s Weaving Blog. I found this blog because I read Dorothy’s wonderful blog.  And Dorothy recently mentioned another blogger and linked to it.  I followed the link.  I skimmed through a few posts and realized that this was a blog to be reckoned with.

I have now started reading Nigel’s past posts more carefully. 

The post that has stopped me dead in my tracks is called “Two Workshop Sessions.”   Go here to read it.  A musician and composer, Nigel describes how he uses binary sequences in composing music. 

I have studied music.  I have even studied composing.  It is not hard for me to follow what he is doing with binary sequences in music.  But weaving? 

Here is what he says about using 4-bit patterns in composing music:

I use 8-bit binary sequences to create rhythmic patterns in the music I compose. I have a library of 4, 8 and 16-bit patterns such as this example from a 4-bit pattern: 1000, 1100, 1111 etc. I then decide how many different patterns I want for a particular phrase or section and how many occurences. I can even build a template like this; a a a b  a b a b and the library system picks a sequence of binary patterns such as: 1000, 1000, 1000, 1101,1000, 1101, 1000.

It is easiest for me to think first in terms of stripes.  A binary system is a system involving 2 units.  So I will work with 2 colors:  B(blue)and BG(blue-green). And I will say that each unit is 1/2” long. So I could do something as follows in designing stripes:

1000 (sequence a)
1/2” B
1 1/2” BG  (3 units x 1/2”)
1100 (sequence b)
1” B
1” BG
1111 (sequence c)
2” BG

And then I would just repeat this.  I think it would be quite pleasing.

Or I could do something a bit more complex. Instead of just having one sequence follow the other, I could vary the final design through repetition and changing the order of these three sequences. To do this, I could create a template, much as Nigel created one.  Since I have three color sequences, the template would be built on a, b and c, a separate letter for each sequence.  I will use this as a template:  a a a b c c b b.

The stripe sequence would then look like this:

(1/2” B + 1 1/2” BG) repeated 3x (a)
1” B + 1 1/2” BG (b)
2” BG x 2 = 4” BG (c)
(1” B + 1” BG) repeated 2x (b)

I made the template up with no particular reason.  I could have used one of the formulas from Dietz’ monograph, “Algebraic Expressions in Handwoven Textiles.”  But that would be a lot more complicated, and right now I am trying to stay with something a little simpler.

Also, there is no reason I couldn’t use different colors in each of the binary sequences. I could use two different colors in each of the sequences.  Or use one color from one sequence + one new color.

Using longer rhythmic patterns and/or more rhythmic patterns, using more colors, using complex templates, well, the possibilities are mind-boggling.

SOME READING SUGGESTIONS

Dietz’ monograph is available for free download here. A very good article by Lana Schneider on the subject is available here.

I found an interesting web page called “An Introduction to Binary Arithmetic.”  I also found an interesting discussion of Pascal’s triangle here.  This discussion suggests several possibilities for using math in weaving.

Related Post:  Designing and Mathematics

"Binary Sequences and Designing" was written by Margaret Carpenter for Talking about Weaving and was originally posted on January 30, 2009. ©2009 Margaret Carpenter aka Peg in South Carolina