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Posted by Jake Wildstrom on December 1, 2007, 1:27 am
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>Having made the pi shawl I'm wondering if there's a pattern based on the
>Fibonacci series?
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
(http://toroidalsnark.net/mkexh2005/mkexh2005-Pages/Image38.html) and
cites the article "The Art of Knitting: Fibonacci and Stripes", by
Laura Bryant, appearing in _Cast On_ in Fall 2003.
One interesting arrangement of Fibonacci numbers, but one that would
be nigh-impossible to knit and at the very least difficult to crochet
would be a spiral assembly of rectangles with Fibonacci-number side
ratios: two 1x1 squares, with a 2x1 rectangle atop it, a 3x2 rectangle
to the left, a 5x3 rectangle below, etc. As I visualized this
initially it'd be stitched-together rectangles, but one could create
this pattern with color simply working from the bottom up (an
inelegant 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
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Posted by Y? on December 1, 2007, 4:13 am
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
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>>Having made the pi shawl I'm wondering if there's a pattern based on the
>>Fibonacci series?
> 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
> (http://toroidalsnark.net/mkexh2005/mkexh2005-Pages/Image38.html) and
> cites the article "The Art of Knitting: Fibonacci and Stripes", by
> Laura Bryant, appearing in _Cast On_ in Fall 2003.
> One interesting arrangement of Fibonacci numbers, but one that would
> be nigh-impossible to knit and at the very least difficult to crochet
> would be a spiral assembly of rectangles with Fibonacci-number side
> ratios: two 1x1 squares, with a 2x1 rectangle atop it, a 3x2 rectangle
> to the left, a 5x3 rectangle below, etc. As I visualized this
> initially it'd be stitched-together rectangles, but one could create
> this pattern with color simply working from the bottom up (an
> inelegant 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
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Posted by hesira on December 1, 2007, 9:17 am
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
On Dec 1, 12:27 am, Jake Wildstrom
show/hide quoted text
> One interesting arrangement of Fibonacci numbers, but one that would
> be nigh-impossible to knit and at the very least difficult to crochet
> would be a spiral assembly of rectangles with Fibonacci-number side
> ratios: two 1x1 squares, with a 2x1 rectangle atop it, a 3x2 rectangle
> to the left, a 5x3 rectangle below, etc. As I visualized this
> initially it'd be stitched-together rectangles, but one could create
> this pattern with color simply working from the bottom up (an
> inelegant solution, but one that's actually doable).
show/hide quoted text
> -Jake
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Posted by Y? on December 1, 2007, 9:46 am
Thnx Hesira, Interesting..
there is alot that can be done with numbers or letters or both combined.
higz cher
show/hide quoted text
> 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
> On Dec 1, 12:27 am, Jake Wildstrom
>> One interesting arrangement of Fibonacci numbers, but one that would
>> be nigh-impossible to knit and at the very least difficult to crochet
>> would be a spiral assembly of rectangles with Fibonacci-number side
>> ratios: two 1x1 squares, with a 2x1 rectangle atop it, a 3x2 rectangle
>> to the left, a 5x3 rectangle below, etc. As I visualized this
>> initially it'd be stitched-together rectangles, but one could create
>> this pattern with color simply working from the bottom up (an
>> inelegant solution, but one that's actually doable).
>> -Jake
>
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Posted by Jake Wildstrom on December 1, 2007, 10:40 am
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>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:
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.
show/hide quoted text
>ABDDD
>CCDDD
>CCDDD
>EEEEE
>EEEEE
>EEEEE
>EEEEE
>EEEEE
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
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>Fibonacci series?