In nature, a relationship known as the “Golden Ratio,” also known as the Greek letter “phi”, produces aesthetically pleasing proportions. We see this played on in the composition of sea shell spirals, the number of petals on a flower, and the arrangement of organs on a human face. Why not use this ratio to create a pair of socks constructed from stash yarn?

A mathematical rule called the Fibonacci Sequence approximates the Golden Ratio. These numbers start with one. One plus one makes two; two plus one makes three. The sequence continues by adding the two final number together. We’ll use this information to guide both our choice of materials and our knitting process.

From your stash, select sock yarn colors that play well together. Being a bit of a minimalist, I like to work with two or three colors, but you can also use five or eight (both numbers on the sequence). Gather together around six hundred yards, and then determine a color arrangement. For example, if I have two balls of navy and partial balls of red and green, I will use the navy for the cuffs, heel, and toes; I might also decide to work stripes in a navy/red/navy/green sequence to create a pattern with the colors.

We’re going to make a stockinette sock with two by two ribbing at the cuff, a short-row heel, and simple toes ended with the Kitchener stitch. Measure around the ankle to determine the size of the tube; multiply this number by the gauge to get your stitch count, and round it to a multiple of four. Ladies’ socks knit at fingering gauge will usually require between sixty and sixty-eight stitches, while men’s socks may go up to seventy-two or seventy-six.

To avoid complete randomness, I plan to match the cuffs, heel, and toes; if my yarn supply allows, I like to have all three areas in the same color. Casting on, I knit a k2,p2 cuff. Small-footed socks look good with eight-row cuffs, while larger ones can handle thirteen rows.

At this point, I am ready to introduce controlled randomness to the project through the use of a six-sided die. Because I want to use Fibonacci numbers, I use the following as guidelines:

Roll of 1… 21 rows
Roll of 2… 2 rows
Roll of 3… 3 rows
Roll of 4… 8 rows
Roll of 5… 5 rows
Roll of 6: 13 rows

This selection of numbers ensures relatively wide stripes, which reduces the number of ends to weave in later on. Roll the die to determine the size of each stripe, but use your sequence to add order.

Using the colorway from above as an example, I knit an eight-row cuff in navy. I then roll the die and knit a five-row stripe in red. Then I roll again and knit an eight-row stripe in navy, a three-row stripe in green, a thirteen-row stripe in navy, and so on and so forth.

When the leg is at the desired length, I come back to navy, knit five rows, and then short-row the heel, following this with three more rows of navy. This makes an eight-row stripe that visually connects the sides of the sock. I return to using my die here, determining that the foot will consist of a five-row stripe in red, a three-row stripe in navy, a thirteen-row stripe in green, a five-row stripe in navy, and so on until I am ready to work the toe.

To avoid “second sock syndrome,” randomize the stripes again. Your finished pair will “match” because of the shared cuff, heel, and toe hue as well as the fact that the stripes repeat in a color sequence, but the use of the die to determine the size of each stripe will keep the knitting interesting. Or, if you prefer, use the first sock as a guide to stripe width but start the color sequence at a different point. When the pair is finished, you can celebrate your stash-busting and ingenuity with a pair of interesting if not perfectly matching socks!