How to crochet a fractal

This article will (unsurprisingly) tell you how to crochet a fractal

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Here are some instructions describing how to crochet a fractal without the maths included in the article Crocheting Fractals by Felix Stokes in issue 10.

Recommended supplies:

  • 4mm crochet hook
  • Double knitting yarn

Unfortunately, it’s difficult to describe how to make this shape using a conventional pattern, because it’s essentially all just one long complicated row. Instead, below you can find a walk-through of making a small first iteration triangle, and once you’ve made that it should be clear how to expand up to larger iterations.

Crocheting a simple fractal

The first step is to draw out a diagram of the triangle you want to create, then trace out a path that goes over all of the lines. Below is an example where the diagram is in blue dots and black lines, and the path has been drawn in red, starting from the top.

Next, you need to work out how long you want each side of the smallest triangle to be (ie the distance between two blue dots). I made mine 5 stitches. Then, chain however many stitches that is, place a marker, and trace over one section of the path on your diagram in a different colour. You’ll want to repeat this until your path connects to itself. For example, after 10 stitches my diagram looked like this, I had reached point 2, and I had placed two markers:

When you have placed 5 markers (and have therefore reached point 5 on the diagram), chain another 5 stitches (or however long your sides are), then place your hook into the stitch marked by your 3rd marker, and make a slip stitch. Chain another 5 following your path, and make a slip stitch where your 1st marker is.

Continue tracing out your path as you go to keep track of where you are. You’ll want to chain another 5, slip stitch at the 5th marker, chain 5, then connect up to the start. And voilà! You should be done!

Crocheting any fractal

To make larger iterations, the process is essentially the same. Draw out the triangle you want to make, trace out the path you’ll need to follow over the top, then trace over the path in a different colour as you go. Note—the first line you chain will need to be the entire left-hand edge of your overall pattern. Otherwise, you won’t be able to connect up your chain in the right places later. Have fun!

Felix is primarily a classics student at Oxford who loves knitting, crochet, and all things yarn. He’s also a huge fan of topology, making mathematical craft one of his favourite hobbies.
+ More articles by Felix

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