A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?Leonardo Pisano Fibonacci, 1170-1250
Liber abaci, 1202
The answer lies in a sequence of values known today as Fibonacci numbers:1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …
Each number in the sequence is the sum of the two preceeding numbers. The sequence itself has been referenced in many areas of science and mathematics.
So what does this have to do with designing stripes?
The theory is that using any of the numbers in the sequence to define the width of a stripe creates the illusion of a random pattern that’s visually appealing. I’ve never heard an explanation as to why this would be true, but I suppose it has something to do with the three primary characteristics of the sequence:
- Two of every three values in the sequence is an odd number.
- With the exception of 1 and 2, no number in the sequence is the exact double of another number.
- With the exception of 3, 21 and all even numbers which are always divisible by 2, there are no numbers in the sequence that are an even multiple of any other number.
Having always felt that my designs were too symetrical, I decided to try out this theory. I had already chosen four yarns in pastel shades to make a baby blanket. While I wanted the overall pattern to be a small plaid, I also wanted the colors to flow through the blanket. To keep the plaid small, I decided to limit my design to the first few numbers in the sequence with no more than 5 threads in any stripe.
I wanted to have a repeatable design in my pattern; otherwise, I ran the risk of making frequent mistakes and only had a limited amount of time to get the blanket done. Ideally, I wanted to be able to determine the number of consecutive threads to weave in a certain color by simply looking at the previous stripe of the same color. So my first decision was that the width of the stripes for each color — any color — would be 1, 2, 5, 3 and 1.
My next goal was make sure that two adjacent stripes contained a different number of threads. I particularly did not want to have two stripes of the same size next to each other. So I decided I would use an offset technique to interleave the five stripes of each color with two stripes of the colors on either side. I was hoping this method would get the colors to flow through the blanket. I now wish I had taken a picture of the finished blanket because the resulting plaid was interesting and subtle in pale yellow, blue, green and white. The layout for the stripes is illustrated in the following image:
I recently used the same pattern of stripes for a felted bag I knitted with four bold colors of Lite Lopi. This time, I chose to have a dominant background color with very distinct foreground stripes. It’s still an interleaved 1-2-5-3-1 pattern, but the background color is repeated more often for a slightly different effect: