Leigh's Fiber Journal: Fibonacci

Showing posts with label Fibonacci. Show all posts

Monday, December 24, 2007

House Socks

Done!

I have to admit that I lost these for awhile so that I was a little late getting them done. I had hidden them away Thanksgiving week, as Recipient was here all week. In my general straightening up and furniture rearranging, I put them somewhere and promptly forgot exactly where that was. I finally found them last week, tucked away on my bookshelf. Whew. I couldn't imagine what in the world I'd done with them.

These are the cuff down, the Red Heart worsted weight ones. A lot of you responded to my wondering how well acrylic yarns worked for socks, saying that the problem acrylic is that doesn't allow feet to breathe. Hence sweating can be a problem. Of course I won't mention that to Recipient, who won't wear them in shoes anyway. I'll be curious as to how they wear.

Like my Summer Socks, these are knitted from three different yarns. This time however, instead of cutting the yarn and having a lot of ends to weave in, I took Bettina's suggestion and carried the yarn up the stripes. This did create some rather long vertical floats on the inside, which hopefully won't get toes or toenails caught in them. However it sure did make knitting and finishing faster and easier. A good thing too, since they needed to be done before Christmas.

The stripes are a Fibonacci sequence of 2, 3, and 5. By using three colors and alternating them as you see, I had a pattern that I was happy with.

My family celebrates Christmas, so no matter how you and yours celebrate this season, I want to wish all of you a very happy one!

Thursday, June 07, 2007

Fibonacci Overlay 2

My second summer & winter Fibonacci overlay experiment is off the loom. Like the first, I didn't match the colors of my warp stripes to the threading pattern.

My threading pattern was the same Fibonacci threading sequence I've been using:

1 unit for block A (threaded 1, 3, 2, 3 making 4 ends for 1 unit),
2 units for block B (threaded 1, 4, 2, 4 making 8 ends),
3 units for A (12 ends),
5 units for B (20) ends),
8 units for A (32 ends),
repeat

For the colored stripes in the warp, I used a different Fibonacci sequence so that it overlaid the threading sequence. I made it easy on myself and used a sequence of three: 8 warp ends of white, 12 warp ends of dark green, and 20 warp ends of dark purple. My warp is 8/2 unmercerized cotton.

I put on enough warp for three dishtowels, and then used what was left to experiment a little. For each dishtowel, I used different colors in the tabby and pattern wefts, and different treadlings as well.

For the first one I used purple tabby weft (same as warp, an 8/2) and white pattern weft in 6/2 unmercerized cotton. I treadled with the same pattern as the warp color stripes: 8, 12, and 20. You can see these changes in the horizontal bands of the weaving above.

For the second dishtowel, I continued to use the 6/2 white cotton pattern weft, but switched the tabby weft to the 8/2 green cotton. I changed the treadling to be the same sequence as the threading blocks, using 4 pattern picks (each of first tabby and then pattern wefts), 8 pattern picks, 12 picks, 20 picks, and 32.

For the third one I used a white 8/2 cotton for the tabby and navy 6/2 cotton for the pattern wefts. I repeated the 8, 12, and 20 treadling pattern.

After that I had a little warp left and so tried another traditional summer & winter treadling. I used the 6/2 white for the pattern weft again, but this time used an 8/2 navy unmercerized cotton for the tabby weft.

In some ways I think the navy was a better choice for the tabby weft as both the green and purple I used in the warp have blue as a common color element. It had a better visual influence on both the green and the purple, which tended to muddy one another a bit when used on top of each other.

One thing bugged me while I wove was the white warp stripes. I figured that I should have learned my lesson with that last batch of towels as white tends to be very pronounced against darker colors. As I wove, the white kept grabbing my attention and was a distraction. I kept mentally kicking myself for using it in the warp. But now that it's all off the loom and I'm looking at photos of the result, I realize it isn't so bad. Hmmm. Live and learn.

In reading all this over, I realize that one problem with reading about weaving is that it requires a lot of concentration to mentally visualize what's being described. It does for me anyway and I don't know about you, but I'm not always up to it! So if my descriptions are are confusing, just enjoy the pictures. :)

by Leigh at Leigh's Fiber Journal

Fibonacci Overlay 1
My Fascination with Fibonacci
Summer & Winter: Structure and Theory

Monday, May 28, 2007

Fibonacci Overlay 1

Originally I thought that after I'd woven this set of Fibonacci dishtowels, I'd put on a new warp with a different threading plan. My brain had other plans however. I find that once I get a weaving rhythm going, my mind begins wandering on a "what if" sort of game. So here is the first of two ideas that use the same Fibonacci threading plan. The first idea uses an overlay of even color stripes. Each color group has 20 warp ends in it. You can get an idea of what I mean in this photo:

My color warp stripe idea with Fibonacci threading.

You can see from the horizontal lines, that I changed the treadling pattern in the same frequency as the stripes of color. The colors don't match up with the threading blocks, and the result is another complex looking fabric with simple elements.

Here are my results. These are all summer and winter, a two shuttle weave.

Dark blue tabby weft and white pattern weft.

Turquoise tabby and white pattern wefts.

Turquoise tabby weft and white pattern weft.

The color stripes are especially noticeable in this one as both tabby and pattern wefts are white. The white stripes are predominate and what you can't see from these photos is the texture created by the heavier pattern weft. Here is a close up to try and show the subtle visual variations from the texture:

Color combinations and texture are the two things which intrigue me about the Summer and Winter weave structure. They make the possibilities seem endless!

The last one I did introduced a color which wasn't in the weft:

Turquoise tabby and light gray pattern weft.

This one surprised me. At first I didn't like the gray, but now it's my favorite one.

So that's it for that experiment. I have one more idea to try by tying on to this same warp. After that it will be time to move on to something different.

Thursday, May 17, 2007

Summer & Winter: 2nd Dishtowels

By Leigh

Finally, a weaving update. Not that I haven't been busy weaving, but seven dishtowels from the same warp doesn't make for much news. I have been weaving this warp, the multicolor one of navy, lime green, and cinnamon brown in 8/2s cotton.

For the pattern weft, I used a 6/2 navy cotton for all of the dishtowels. My experimentation involved the tabby weft, trying different colors and different color combinations. Here are the results.........

1 - Tabby weft in lime green

2 - Tabby weft in cinnamon brown

3 - Tabby weft in navy blue

4 - Tabby weft in dark green

Then I tried using two colors for the tabby weft, alternating colors with each block.

5 - Alternates lime green and navy blue tabby wefts

6 - Alternates cinnamon brown and navy tabby wefts

7 - Alternates lime green, cinnamon brown, and navy blue tabby wefts

If alternating different colors seems like a lot of work for dishtowels, it is. Of course, my goal was not specifically making dishtowels, but experimenting with summer & winter, and, in this case Fibonacci. Sharon had commented that these looked like they'd make nice sofa pillows and I have to agree with her. Now I am mentally planning a pillow project in the near future.

I have to admit that when I first pulled these off the loom and popped them into the washer, I thought they all looked pretty much the same. Comparing the details of them here though, I can see how different they are, albeit subtle.

What intrigues me about summer & winter is the interplay of color. There are quite a few possible combinations with only four shafts. The warp and the two wefts combine visually in a fun and fascinating way. Even so, I think these are a little dark for dishtowels, though I'm sure that is a matter of personal taste. At any rate, I'm tired of looking at these colors and ready to move onto something else!

Thursday, May 03, 2007

My Fascination with Fibonacci

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.

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.

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

Tuesday, May 01, 2007

Summer & Winter: Experimenting with Multicolor Warp

Even though I've been busy spinning the Bowmont fleece, I've been busy with my weaving too. I'm still experimenting with summer and winter, this time with a multicolor warp.

I have to say that these are not colors I would have chosen to use if I were designing from color theory formulae or color combinations from inspirational photographs. These colors are the result of designing strictly from my stash. I've picked up a lot of mill ends and leftovers from other weavers. Consequently my stash consists of a hodge-podge of colors and yarns of various fiber contents. On the one hand, as a weaver who feels that a lot of her experiments are flops, this is a good thing as this way I don't fret over wasting yarn if I have a few failures. On the other hand, it limits what I can do, as my odds and ends don't always seem to go together.

My method of choosing color combinations is to pull out all my yarns which are of the same size and fiber content. These are set out somewhere; on shelves, a table, or even the floor, where I can look at them, stare at them, contemplate them. I arrange and rearrange cones of yarn in various color combinations until something finally "works." Sometimes it takes days before I finally decide that I either like what I'm seeing or I don't. I can't explain it.

So, using the above combination of 8/2s navy, lime green and brown cottons, here are the first two in a series of about six.......

This one is using the green for the tabby weft and navy blue for the pattern weft.

And this one is using brown for the tabby weft and navy for the pattern. The colors, I'm afraid, aren't completely accurate. They aren't even consistent with one another, I think because they were photographed at different times of day. These are in the same Fibonacci sequence that I've been using for my other dishtowels and polychrome rugs.

As I sit and weave, another mix of yarns sits on the desk where I can watch it. I weave and think, and weave and plan. What a lovely way to spend the afternoon.

Sunday, April 15, 2007

Summer & Winter: Polychrome Rug 2

Thank you, All, for your good wishes on my first year of blogging. I have a quick question about my new template, and would appreciate feedback. I use the Firefox web browser, but checked my new look in Internet Explorer 7 (since different browsers tend to do different things with the codes). I was dismayed to see that in IE7, the blue line at the top overlaps the bottom of my title and description. I couldn't figure out what to do in my template about this, especially as I found that the overlapping didn't occur in the preview window. Is anyone else seeing these overlapped?

Now, here's what I want to show you......

This is my second rug in polychrome, using the same threading as the first one. It measures 19 by 31 inches, plus 3 inch fringes on either end. Of course, I was silly enough to ignore the wise advice I have heard repeatedly, "Always put on more warp than you think you'll use," and had to tie on more to weave this one.

Marie asked about the rug filler I used. Yes, it does look like mop cotton!

Now, I did not purchase this, it came from the weaver from whom I bought my loom, who included all her weaving yarns too. I suspect the wrapper is exceptionally out of date; indeed, I wouldn't even know where to get this stuff.

It is a 4 ply worsted weight cotton yarn, similar to the sugar & cream type crochet cottons. It measures 12 WPI (if one thinks like a spinner) or 750 yards per pound (if one thinks like a weaver).

It does not make for an especially thick, nor sturdy floor rug. It would probably do best in low traffic areas or as a run-and-slide cat toy across a hardwood floor. I think it would be better suited for heavy blankets, or a throw across the back of a chair than for the floor. But what the heck, I just used what I had. In fact, I would never have purchased this color combination, I just challenged myself to use what I had. It took quite a bit of experimenting to come up with a color scheme that I liked, but once I got weaving, the spring-like Easter colors grew on me.

I took both my little rugs to the monthly WNCF/H Guild meeting where, in preparation for the program on rug hooking, the show-and-tell theme was "rugs."

Show & Tell rugs at the Western North Carolina Fibers/Handweavers Guild meeting.

Quite a few gorgeous rugs to admire, as you can see. Lots of good ideas to tuck away for future use. I can't say that I see myself as a rug weaver, but I do like the idea of creating items which are both useful and functional. So ........ maybe someday ........

Tuesday, April 10, 2007

Summer & Winter: Polychrome Rug 1

I finished this little rug over the weekend. Annie Ham of The Netherlands, who led the Online Guild's Summer & Winter Weaving Workshop closed the month out with a handout of various treadling possibilities for summer & winter. The first was polychrome. After my polychrome sample dishtowel, I wanted to explore this a little further.

The idea to do a small rug came because April's meeting of the Western North Carolina Fibers/Handweavers Guild will feature a rug themed show-and-tell, since April's program is on rug hooking.

Here are my rug's particulars:

Warp - 10/4 cotton rug warp
Sett - 12 epi
Pattern weft - 4 ply crochet/rug filler cotton, alternating 3 colors.
Tabby weft - 6/2 cotton
Threading - 2 block S&W with repeating 1, 2, 3, 5, 8 Fib stripes
Treadling - as drawn in
Finished size - 20 by 32 inches plus 3 inch fringe

Ordinarily I wouldn't choose to use these colors; I just used what I found in my stash. I had to experiment a little, but am happy with the result!

What makes polychrome a little different from traditional summer and winter treadling is rather than alternating pattern and tabby shots, two weft picks (of different colors) are thrown and then the tabby shot. The resulting effect is a lot of fun to weave. One's mind goes on and on with endless possibilities!

Friday, April 06, 2007

Summer & Winter: 1st Dishtowels

By Leigh

After I completed my summer & winter sampler from the Online Guild weaving workshop, I decided that I needed to go back to the beginning and work more slowly through the workshop notes. Samplers are fun to weave and an excellent way to explore ideas and to test yarns, colors, setts, shrinkage, etc., but I find that if I really want understand a weave structure, then I need to spend some time working with it. It is not only my head which needs to understand it, but my hands and feet need to understand it as well. So I went back to my idea of weaving dishtowels as samplers.

I warped my loom in 8/2 lime green cotton, set at 16 ends per inch; enough for 6 dishtowels. My tabby weft was the same as the warp, and my pattern weft was a navy 5/2 cotton. I threaded a simple repeating Fibonacci sequence (1, 2, 3, 5, 8) and treadled it the same way, aka "as drawn in." I previously shared the threading for two block summer and winter with you in this post.

The tie-up I used is on the left. I believe that it is pretty standard for a four shaft, six treadle loom. The first two treadles on the left alternate to create the tabby weave. A tabby shot is thrown between each pattern shot.

With this tie-up, I wove through the four basic summer and winter treadling ways, and then tried two more for the last two towels.

First is the traditional way of treadling which close-up, makes the weft look something like bricks in a wall. (Can't see it from this photo I'm afraid.)

The pattern is treadled by alternating the pattern shafts, 1-2-1-2. So one block is woven on treadles 3 and 4, the other on 5 and 6, each time with a tabby shot thrown between.

Next is the X's treadling, which requires paired pattern shafts, 2-1-1-2. So one block is woven on treadles 3 and 4 (4-3-3-4), the other on 5 and 6 (6-5-5-6), each time with a tabby shot thrown between.

You can see the X's in that pattern above. I liked the look of that one.

Then I wove a towel in the O's treadling, which is also a paired treadling, except that it starts on the other pattern shaft. So it is treadled 1-2-2-1.

One block in treadled 3-4-4-3, and the other, 5-6-6-5, with the tabby shots in between. You can see the O's in the above photo.

The thing about the X's and O's is that since summer and winter is a reversible weave, then no matter which of them one weaves, the other appears on the back side. While I like the X's pattern better, I found that the O's was easier to keep count of while I was weaving.

The one I really like, however, is the dukagång treadling, which weaves columns.

It can be woven two ways (on a four shaft loom) by choosing either the first pattern shaft or the second. Mine was woven by simply alternating the 3rd treadle with tabby, or the 5th treadle with tabby, depending upon which block I wanted to weave. I could have used the 4th and 6th treadles if I'd preferred. But I didn't.

The next towel I tried in polychrome, which is a variation of summer and winter which requires two pattern weft colors in addition to the tabby. Each color is shot, and then the tabby, so that the tabby shuttle is thrown every third pick.

At this point I hadn't figured out how to alternate for the blocks, so I wove stripes, but I really liked the effect and immediately started the mental planning for a polychrome project. In addition to the lime green tabby and navy blue weft, I added a dark gray 5/2 cotton for my second pattern weft and got the above result.

After this I had enough warp for one more dishtowel, so I switched the tabby and pattern wefts, using the lime green for the pattern shots, and the navy for the tabby. This resulted in a muted effect, below.

These barely scratch the surface of what can be done with summer and winter, and I have the feeling that I may be spending a long time exploring the possibilities.

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