I am weaving fabric and want to make a double fibonacci to represent the theme I am working on for a contest on fb.  I saw this great double fibonacci pattern and would love to do the same but cannot figure out how to do it.  I have PixeLoom and iWeaveit and could stumble my way through it but thourght someone might have a better system.

Here is the link to the project I saw:  http://wanderingweaver.wordpress.com/tag/double-fibonacci-stripes/  If you scroll halfway down you will see what I am trying to mimic.

I appreciate any suggestions or help with this.

Thanks,

Claudia

Here's a photo 

Comments

Tue, 09/24/2013 - 15:18

tommye scanlin

I use Fibonacci sequence frequently when designing, even in pictorial tapestry work.  It gives a starting point for numbers of items to include, for instance.  Perhaps I'll place eight feathers rather than six or seven in a design.  Maybe I'll make the size 3 ft. x 5 ft. in proportion, let's say.  In stripes, I determine the size of the 1 unit... whether it represents 1 thread or 1" or anything else, then plan the sizes of other numbers selected from the Fibonacci numbers using the size of the 1 as the guide.  There's a fascinating website with many, many examples of how the Fibonacci numbers are seen in math (of course) and nature at this link:  http://www.maths.surrey.ac.up/hosted_sites/R.Knott?Fibonacci/fib.html

Tue, 09/24/2013 - 16:02

mneligh

I've done several pies on fibonacci squares or stripes, both patchwork (pieced) and woven.  That was before I got into network drafted sine waves, etc.  What weave structure do you want to use?

In plain weave the threading order would be 

color a - 2  threads

color b - 13 threads

a - 3 threads

b - 8 threads

a - 5 threads

b - 5 threads

a - 8 threads

b - 3 threads 

a - 13 threads

b - 2 threads.

Expand this according to the series. 

 PM me if you want more information or other weave structures, more expansion, etc.

Tue, 09/24/2013 - 16:20

kerstinfroberg

If what you are after is how to enter the colour sequence in the weaving software, I don't think any would generate such long sequences automatically. Otoh, if you are using a simple structure, you will be fine "just" having the sequence on paper (where you probably would have it anyway, to begin with).

If you are doing (say) twill blocks, I suppose the same applies: you will need a list on paper first.

Tue, 09/24/2013 - 17:19

Claudia Segal (not verified)

I forgot to add the rest of the info. I am using 8/2 cotton sett at 20 epi and weaving plain weave. What I need is the counts. How do I know where and when to intersext to two fivonacci sequences and how do I create the sequences? Has anyone done this with formulas in Excel? TIA Claudia Width of the piece is about 30" or 660 ends
Tue, 09/24/2013 - 18:14

mneligh

I write my own software to figure out complex drafts.  This one can be solved with graph paper or a simple number line.  You could use a yardstick as a number line.  

On a piece of paper, start writing out your series.  Make sure you leave the line below the numbers blank if you have to wrap.  It's like this: 1,1,2,3,5,8,13,21, and so on.  Each time you write a number in the series, move a pin that many 16ths of an inch down the line.  (On graph paper, advance that many squares.  Or start with a pool of 330 beans, and remove that many beans from the pool each time, keeping the piles of beans separate.)  Stop at 330/16ths, or about 20 inches, 330 squares, or when your pool of beans is exhausted.  The next number in the series is the current number + the previous number, so the number after 21 is 13 + 21 = 34.  

Write the last number under the first 1, etc.  Up above I skipped 1 because it is problematic in some weave/structure cases, but you can use it if you like.

Hope this helps.

Tue, 09/24/2013 - 19:26

kerstinfroberg

The "beauty" (if you like "number magic", that is) is that you can think up many different ways to implement the basic system. (admittedly, it takes some calculating/scrabbling/fiddling - ) Several years ago, I was participating in a Complex Weavers study group (maybe called something like "math and weaving"?) - my system was/is based on Pascal's triangle, but you might get some ideas of how to apply a "system" to make a "reality"(ie warp) - here is my article.

(BTW, mneligh: I really like your idea with 330 beans - except for having to count them ut :-)  Cally just confessed she can't count to 10 - I haven't "gone public", but it *has* happened I can't count to 4...)

Tue, 09/24/2013 - 20:27

mneligh

I count in groups of 4 (or sometimes 5).  My favorite graph paper for designing network weaving drafts is based on 8 small squares = 1 big square.  I thread in groups of 4 -> slipknot, and tie on 2 of those for each knot on the apron.

I'm not sure I could count to 330, except in groups of 5 beans it's 33 piles of 2 groups of 5 each.  The 33 breaks down into 6 groups of 5 piles plus 3 left over . . .

Tue, 09/24/2013 - 23:48

sandra.eberhar…

If what you are looking for is a plaid (double fibanocci?)  treadle the same way you threaded.  I used block twill for a Fibanocci plaid in two colors.

Wed, 09/25/2013 - 00:17

SallyE (not verified)

Like Bigwhitesofadog, I also have done "double" Fibanocci simply by putting the Fibanocci sequence in both the warp and the weft.   Here is the posting of what I did, using a twill pattern:

http://weavolution.com/project/sallye/fibanacco-plaid

Another way to get it to "fade" from one color to the other is to simply pick a number and warp in sections of threads using that number.  Each section uses one less of color A and one more of color B in each section.   Here is what I did using the number 17:

http://weavolution.com/draft/prime-number-17

 

 

 

Wed, 09/25/2013 - 01:14

mneligh

If you look at the picture, she means fibonacci increasing on one color while decreasing on the other along the x axis.  That is, the sequence appears only in the warp.

I too have done double (x & y) fibonacci, in plaid, in double weave, in satin, in patchwork, in taquete.  The coolest thing is that as the numbers get small it looks like it disappears down a drain if you make it bilaterally symmetrical.

Then there are sine waves and their variants . . . and Pascal's triangle (see Kerstin's note above), and hyperbolic paraboloids, and other functions.  

The last piece I did in this series was de Broglie waves with a color shift from white through colors to black as the wave length shifted, representing the light from a star.  It was 4' x 6'.  The weft was all hand spun from 2 fleeces.  Then a series of weddings forced me into krokbragd rugs . . . no doubt I'll come back to more math, but I need to talk to my son the physicist to get more ideas.

Wed, 09/25/2013 - 16:58

JacRoyce

Just wanted to say that this thread makes me happy. I also love to use iterated algorithms when I'm designing rugs....

Sun, 09/29/2013 - 17:07

Cally (not verified)

...I thought I had better chip in and see if I can salvage my reputation! You can do a 'double Fibonacci' from any point in the sequence you like: there is no right or wrong place to start. Each Fibonacci 'unit' can also be a single end or a group of ends. The main things to think about are the total number of ends you want, and do you want the sequence to extend all the way to the edges or do you want to have solid colour at the edges and a blended area in the middle. 660 ends is quite a lot for just one colour change, so another option to the 'solid edges, blend in the middle' is to progress through three or four colours.

 

To work out the number of ends I need in one progression, I simply choose a likely place to start. I pick a Fibonnaci number, say 13 ends of colour A. Then I add 1 end of colour B. Then I alternate between A and B, in each case moving to the next Fib no for that colour (decreasing along the sequence for A, increasing for B). That would give me a total of 66 ends by the time I had switched completely to 1 end of A and 13 of B. 66 is quite a good number for your purposes, because if I substituted 10 ends for every 1 in this sequence I would have an ordering of 660 ends! The narrowest stripe would be 10 ends, or 1/2 an inch. If you don't like that, then try starting with 21 ends of A, or 34 ends of A - it doesn't matter where you begin, as long as you then introduce 1 end of B and follow both sequences in opposite directions until you reach the other end.


Sun, 09/29/2013 - 17:20

Cally (not verified)

I knew I had a handout somewhere... below is an illustration of the process I tried to describe above. Once you have the basics, you can adapt it freely, e.g. multiplying the base numbers by a certain number of ends per group, or repeating the sequence across the cloth changing from one colour to another, or anything you like really.

Mon, 09/30/2013 - 20:04

Claudia Segal (not verified)

Thanks Cally

That's exactly what I was looking for!  My only other question is, if you start with 60 of say blue and 1 of red how can you be sure you will have all 660 ends the project requires to be wide enough?

Claudia

Mon, 09/30/2013 - 20:19

mneligh

You could use the bean or numger line method I suggested above.  I said 330 because you only need to figure out the sequence for half the numbers since the other half are the same only in reverse order.  Sixty is not a number in the sequence: 1,1,2,3,5,8,13,21, 34, 55, 89, 144, etc., unless I added wrong.  

It won't come out at exactly at 330 ends.  

Mon, 09/30/2013 - 21:27

Cally (not verified)

Yes, as mneligh says, you only need to work out half the total. Since the other sequence will be the same, but in reverse order, the two colours will have exactly the same number of ends. I would try

 

- adding up the Fibonacci numbers until you get as near to 330 as you can. The highest F no in that sequence would be the number of ends you want to start with in colour A.

 

or

 

- choosing a smaller total which is a factor of 660 (like 330 or 110), halve it and do the same thing. You would still take the highest F no in the sequence as your starting point, but multiply each F no by the divisor. This might be an easier way of hitting the exact target - we already know it works for 66 by starting on 13!

 

Cally

Tue, 10/01/2013 - 01:22

mneligh

The numbers really do matter -- human perception seems to be based on them.  The classic experiment involves candles.

Take one candle and look at the light it sheds on a piece of paper in a dark room.  Add another candle to it (total 2) and the difference in shed light is immediately noticeable.  To the 2 add one more.  You still notice the difference.  If you add one more (total 4) you don't notice the difference.  Add one more, and you don't notice the difference between 4 and 5, but you immediately notice the difference between 3 and 5 and so on from 5 to 8, 8 to 13, etc.

This is why so much art is based on this number series -- it's special.  It doesn't happen with prime numbers or any other series.  This one is magic.  So while you can start with any arbitrary point in the series, you must start with numbers in the series, or multiples of them.  

Tue, 10/01/2013 - 13:56

mneligh

If for some reason you had to have 60 threads in a single block, you would have to project the sequence backwards and then forewards. 

60 = x + y, x = y + z, y = z + a, etc.

It's easier to write a small program to do this than to set up excel to do it, but those are the formulae you would use.   I could write pseudocode to do this, but I would use an array to store the series.  Anyone up for that?

Tue, 10/01/2013 - 14:39

Claudia Segal (not verified)

Yes, I am up for writing code to help with adding the numbers in the Fibonacci series so I come out close to the 660 threads I need for the project.  So, 330 in a single finbonacci series and the complementary 330.  I want my finished project to look like the photo I posted in my first post.

Thanks, everyone, for all your help.  I feel as though we are almost there.  I keep thinking there must be a formula or formulae to create this design.

Claudia

Tue, 10/01/2013 - 15:03

SallyE (not verified)

You can do this easily in Microsoft Excel:

In cell A1, put a 1.   In cell A2, put a 1.  

In cell A3 put this formula:    =A1+A2

Now copy that formula into the cells below (column A), and you will have the Fibonacci sequence that is as long as you like.

 

 

Tue, 10/01/2013 - 15:13

mneligh

If you want 330, I have already given you the sequence above: 1,1,2,3,5,8,13,21, 34, 55, 89, 144 

It comes out to 376 as the sum. The formula is 

F_n = F_{n-1} + F_{n-2},\!\,

 You could also consider 2, 3, or  4 to be your "unit", so the sequence might be 2,2,6,10,16,26,42,68, etc

If you look at Cally's post #13, you just need to extend the draft using this sequence.


Tue, 10/01/2013 - 15:59

SallyE (not verified)

Or you can add a column B to the spread sheet, starting with cell B2, and put in the formula:

=SUM($A$1:A2)

Copy that into the cells in column B, and you get your sums for every Fibonacci sequence to that point.

Tue, 10/01/2013 - 16:24

mneligh

All true, but we've already given her the sequence.  For such short sequences I typically do them in my head.  Even if she wanted 1000 ends instead of 330, it's less work to me to just use the calculator function of a computer with the number pad than it is to type in a spreadsheet.

I'm very lazy.