Thursday, May 03, 2007

My Fascination with Fibonacci

By Leigh

Is everybody familiar with this Fibonacci stuff? How in 1202, Italian mathematician Leonardo Fibonacci of Pisa published a hypothetical math problem about multiplying rabbits and came up with a number sequence known as Fibonacci number sequence (though actually this was known about in India about 450 to 200 BC, see the Wikipedia entry, here.) The really amazing thing is that this sequence is found everywhere in nature. You can read more on that at this site.

For those unfamiliar with it, the gist of the sequence is that starting with zero, each number of the sequence is the sum of the two numbers that went before. In other words, start with zero plus one and add them together. Continue adding the second number of the equation with the sum, and voila, you have the Fibonacci sequence. Like this,

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89
Etc.

Thus, the Fibonacci Number Sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, etc.

My own fascination is probably related to the fact that it is logical. I tend to like things like that: puzzle games, music theory, algebra (though I'm not very good at it). Plus, I love stripes and plaids.

Fibonacci gives a quick and easy formula for stripes, rows, or the placement of a repeating motif. It can be applied to width, frequency, changes in color or texture, whatever. Pull a set of numbers out of the sequence and repeat them, or reverse them, and the result is visually pleasing.

My recently handwoven dishtowels and rugs use 1, 2, 3, 5, 8, and repeat. Since I am weaving summer & winter, I used those numbers to determine how may units each block would have.

Leigh's Fibonacci warp sequence.What has made it all the more fascinating, is that by using 3 colors in my warp, each repeat of the sequence begins on a different color, as you can see. As I weave, I can treadle stripes like this, treadle the same 1, 2, 3, 5, 8 sequence as in this rug, or do something else as I did here. So not only can I have Fibonacci stripes, but Fibonacci plaids too.

As I weave I am also experimenting with different colors not only in the warp, but for the weft as well, both for the pattern and the tabby. And as I watch the colors and textures reveal themselves, my mind runs wild with new ideas.

I've also begun to wonder about repeating these squares and rectangles with fabric for quilt squares. Probably not something I'll try any time soon, but something to think about nonetheless.

Posted 3 May 2007 at http://leighsfiberjournal.blogspot.com

Related Posts:
Fibonacci Overlay 1
Fibonacci Overlay 2
The Gestalt of Weaving (or Spinning, or Knitting, or ........ )
Stripes!

10 comments:

  1. Fibonacci is also used in architecture (window configuration comes to mind) and you can find it natually in things like the curve of a snails shell, amoung other things. I was glad to see you mention this as I used to use it alot when I did quite a bit of weaving when we lived in Kansas. It really does aid in the creation of mind-appealling formations in one's weavings - as you so wonderfully illustrate in your towels, Leigh!

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  2. It is interesting and probably because Fibonaci is the architecture of nature, that most people find it pleasing to look at. One of our building blocks, common to all. Beautiful dish towels. Can imagine them for display only.

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  3. Hey, Leigh- If you do set up an aquarium (enable enable enable), let me know if you want a few panda cories!! ;-)

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  4. re: the new microwave brightening my kitchen... well it does seem to go better. But the first picture is pretty dark because it was the darkened background of another picture. It was originally part of the pictures I took of DD & I destroying her gingerbread house. The kitchen lights weren't on in that part of the room so the background was very dark...thanks to the wonders of digital photography I was able to lighten it up enough to see the old microwave.

    so is the spare bedroom permanently sealed and locked?

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  5. Leigh, having lurked around reading your blog for quite awhile, I feel compelled to let you know how thoroughly I enjoy your writings! If I had been born a twin, you would been the other half, born with all the determination and talent! B2F adventures, for instance, are on parallel paths, yours and mine. What fun! I'll keep reading, so please keep writing!! How you find the time amazes me...

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  6. Donna, I'm so glad you decided to comment and introduce yourself. It's nice to know I'm not alone in my adventure.

    Renee, the room remains open to kitties but my stuff is kept in safer places!

    Sue, you'll be the first to know if I ever get back into tropical fish. I lament giving away my 55 gallon tank.

    Kathy and Judy, thank you for your insights on Fibonacci! It's something I keep coming back to.

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  7. Very interesting - thanks! I wonder if stripes and such that make use of that sequence are pleasing because we're accustomed to seeing it in nature?

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  8. Thanks, Leigh, for giving me a little more information. When I see larger stripes and people say they used Fibonacci I thought they just picked a number and started from there. Now I know it can refer to blocks or units too. This is helpful as I am by nature unable to do "random". Every time I try I'll do a few randoms placements and then revert to repeating them!

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  9. Leigh,

    I bet both that you will enjoy this article, and that you will readily relate to it.


    http://www.public.asu.edu/~detrie/msj.uc_daap/article.html

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  10. Thank you for the link, Donna. The article is very interesting. I gave it a quick scan at first and am now working through it more slowly. I can easily apply it to web design, and am considering how it applies to textile design.

    I passed the link on to my Computer Design Study Group, which focuses on using computers in textile design, and it has generated quite a bit of comment. Stimulating!

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