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Oct 14

Three Ply Fractal Spinning

After my last post on spinning fractal yarn, I wasn’t quite happy with the idea. The premise of the technique is sound, but it isn’t truly a fractal in the mathematical or scientific sense of the word. A fractal is a pattern that is self-similar, and repeats itself in different scales.

Fractal tree

Image from a thermodynamics article by Alexei Kurakin.

In the traditional fractal spun yarn, you take a braid of fiber, split it in half lengthwise, spin one half of it as is, then split the second half into 2, 3, or 4 sections and spin those end to end onto another bobbin. Then you ply those bobbins together for a 2-ply yarn. That technique produces a stunning variegated yarn, but doesn’t really create a true fractal sequence. This 3-ply technique takes the “self similarity across different scales” to heart and creates a truly fractal spun yarn.

Looking at the figure above, we are following just one path on a branch, where it gets smaller and smaller proportionally.

A braid of dyed fiber in yellow, blue and grey-blue colors

Braid of fiber with bold/distinct sections of color.

For this project I used Polwarth fiber from Yarn Hollow. The bright colors in Lime Sky are perfect for this technique.


Step 1: It’s important to orient your fiber so you spin from the same end in each section.

Step 2: Split the braid in half lengthwise and spin one half from end to end.

Step 3: Split the leftover braid in half and spin it in the same manner as before.

Step 4: Continue in this manner until you can no longer feasibly split the fiber in half.

For this 2 oz braid, I was able to split it a total of four times, giving me five individual lengths of fiber.

Weights of each braid of fiber from left to right: 1 oz, 1/2oz, 1/4oz, 1/8oz, 1/8oz

Weights of each braid of fiber from left to right: 1 oz, 1/2oz, 1/4oz, 1/8oz, 1/8oz

For this example, I Navajo plied to create a 3-ply yarn that keeps the color repeats in sequence. You could leave them as singles as well, but I wanted a slightly more robustly color patterned yarn.

My finished yarn measured to 134 yards of “sport weight” (16 wpi) yarn.

With a self striping braid such as this, you will get smaller and smaller stripes as you work with the yarn in your project.

One repeat of the color striping sequence.

One repeat of the color striping sequence.


Finished cowl, front and back, showing the stripes getting progressively shorter

Finished cowl, front and back, showing the stripes getting progressively shorter

To use the effect of this yarn to its full potential, knitting, weaving or crocheting something rectangular would be best.

Woven fractal-colored yarn shawl on dressmakers form

Reeds and Rushes Cowl

Download the PDF here

Cast on 37 stitches using your favorite method on US size 4 (3.5 mm)

Even rows: knit across

Row 1: (p, k3) X 9, p

Row 3: (p, k3) X 9, p

Row 5: (p, k3) X 9, p

Row 7: (p, k) X 18, p

Row 9: (k2, p, k) X 9, p

Row 11: (k2, p, k) X 9, p

Row 13: (k2, p, k) X 9, p

Row 15: (p, k) X 18, p

Repeat rows 1-16 until you reach your desired length.

Close-up of fractal yarn weaving with yellow, blue and grey-blue striping

Bind off using a slightly stretchy bind off, then sew the two ends together using a mattress stitch or whip stitch. Do this with a light hand to avoid bunching or puckering in your fabric. Soak and block to finish the piece.