Friday, January 30, 2009

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

5 comments:

Holly said...

Thanks so much to the link to Ms. Dietz's booklet. I gave mine away a few years and have been wishing I had it back.

Peg in South Carolina said...

You are welcome, Holly!

Meg in Nelson said...

Right, Peg. I think I'll come back another time. Just dropped by to say hello, but how do I say Hello in binary? I used to know this...

Leigh said...

Very interesting post Peg. I've always been fascinated with Fibonacci sequences in weaving and this is another intriguing idea to explore. Thanks for the links.

Peg in South Carolina said...

Meg, if you used to know this, you know a lot more than I do about binary sequences! Thanks for visiting.
Leigh, yes, I use Fibonacci quite a bit in my designing. These binary sequences are another designing tool entering my tool box.