Fibonacci

Hmm, just worked it out and it would make a very frilly shawl :-)

Number of stitches in the rows:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987

Might try it anyway, just for fun.

Mary

"Mary Fisher" wrote in news:474ea686$0$759$ snipped-for-privacy@master.news.zetnet.net:

i've seen sweater (jumper) & scarf patterns using Fibonacci series for the striping pattern. that would be less frilly anyway. lee

That's true - thanks for the thought.

Mary

Check this pattern out .

Stella

Not exactly answering your question, but I've had my students create designs using the sequence, and most of them come up with stripes, but there are other things you can do. You can just pick a section of the series, like 2, 3, 5, 8, and use them for proportions. Like 2 knit stitches, 3 purl, 5 K, 8, P, repeat. Of course you could do that with any kind of stitch you like. Also, there is a spiral that is the result of the series that results when you make a "Golden Section Rectangle" that is easily done with blocks:

Having made the pi shawl I'm wondering if there's a pattern based on the

I'll have a look, thanks,

Mary

Hi Mary, how about stripes, I did this in weaving a rug once, but because the number of inches got higher than the actual 70 odd ins length, I had to go so far and then I went backwards so I changed the colours as the Fibonacci numbers allowed, can't quite remember if I did up to 13 and returned or just the 8, and returned going backwards down the scale...it was interesting if nothing else.

I'd have to work it out again to get it right, although it should be in my weaving book how I did it.

So stripes could be a way to go depending on how long you want a project to be.

cheers...Cher

Yes, that's what Lee suggested. The scale does increase rather violently :-)

But looking at a flower it doesn't seem as bad as that!

Mary

how or where are you looking at a flower design? Is this a shawl or something? I agree, the spaces between some can go rather steeply leaving you with large spaces between colours, depending I guess on the first number you use.. higz cher

I was thinking of a real flower, not a design, a sunflower is one of the best examples to see. Even better when seeded :-)

Oh right....lol.... I mistakenly thought you were trying to produce a knitted or crocheted or whatever flower and was wondering how to do it using the fibonacci method.

trust me...lol Cher

I trust you, I obviously let my thoughts rule my fingers :-)

Mary

thnx but I meant trust me to be a twit...lol

As others have mentioned, the Fibonacci sequence is used primarily for striping -- it's a pleasing and unusual effect since each stripe is equal in width to the two previous stripes (there may also be some sort of golden-ratio visual aesthetic coming into play as well).

My colleague Josh Holden had a Fibonacci-stripe bag featured in a mathematical fiber-arts exhibition

andcites the article "The Art of Knitting: Fibonacci and Stripes", byLaura Bryant, appearing in _Cast On_ in Fall 2003.One interesting arrangement of Fibonacci numbers, but one that wouldbe nigh-impossible to knit and at the very least difficult to crochetwould be a spiral assembly of rectangles with Fibonacci-number sideratios: two 1x1 squares, with a 2x1 rectangle atop it, a 3x2 rectangleto the left, a 5x3 rectangle below, etc. As I visualized thisinitially it'd be stitched-together rectangles, but one could createthis pattern with color simply working from the bottom up (aninelegant solution, but one that's actually doable). What I'm describing here would look something like this, with at least

4 different colors for regions A-G.

GGGGGGGGGGGGG (8 times) DDDCCFFFFFFFF DDDABFFFFFFFF EEEEEFFFFFFFF EEEEEFFFFFFFF EEEEEFFFFFFFF

There are probably other imaginative ways to fit a Fibonacci design into fiber-craft, but there are what's springing to mind.

-Jake

Very pretty, I've done it in weaving, where I chose a base colour of cream and then put primary colours in as the stripes, idea for a nursery rug.

higz Cher

Never!

M

This can be done with modular squares rather than trying to knit or crochet each rectangle to the correct proportions. You could start with a square module and use different colors for each grouping like this:

ABDDD CCDDD CCDDD EEEEE EEEEE EEEEE EEEEE EEEEE

Notice the proportion created by each grouping: A 1x1 B 1x1 C 2x2 D 3x3 E 5x5

The next step would be an 8x8 grouping down the long side.

You can keep on going and with get a rectangular spiral that has the same proportions as the one I posted earlier.

Hesira

Thnx Hesira, Interesting.. there is alot that can be done with numbers or letters or both combined.

higz cher

That's actually to some extent what I dismissed as "impossible to knit and difficult to crochet", but then, I try to avoid needing to stitch things together, so my notion of what's doable may be more restrictive than others', and I figured the in-line color approach was the easiest way to do this without sewing. However, the idea of using F_n by F_n squares is far superior to my thought of using F_n by F_(n-1) rectangles. Clearly '1' in this diagram, however, has to refer to something more substantial than a single stitch. *g*

A thought I had re doing this sew-free: tunesian crochet might be an interesting way to try doing this, since tunesian leaves a line of crochet-loop-leads at the far right end (left of you're right-handed) of the work, which would be a perfect starting point for a new tunesian block, in a different color, at right angles to the original.

A nitpick: if you want a rectangular spiral, shouldn't E be on top, not bottom? Or, instead of a spiral, one can create a trending effect from upper left to lower right by always placing the new locks on the right or bottom.

-Jake