Introduction to Fractals

The project that I am going to talk about today is rather fascinating because it incorporates the beautiful concept of fractals as it's main color work pattern. The second most interesting part is that it is double knitted, creating a double sided, double soft and thick piece of fabric that fends off the cold very well.

 

The pattern that creates this cowl is the Fractal Cowl by Emily Peters and knitting-wise, it's rather simple and easy to knit. The pattern is very well written and includes elaborate notes on double-knitting, for first timers mostly, so it works well as a first double-knitting project. Beware though! Double-knitting is significantly slower than regular knitting, so don't be fooled by it's stockinette appearance!

One must also pay close attention to the pattern - it's not easy to memorise (not at all actually..), so mistakes can easily happen. I made myself a few, some I could easily fix, but some, being several rows below my working row, not so much. The yarns I used have low contrast between them so the mistakes are not at all visible and I was lucky in that aspect, otherwise I would have to frog and re-knit or keep looking at a destroyed pattern.

Usually small mistakes in color work patterns can be overlooked as "aesthetic creativity", but not in this case. The reason for this is because we are knitting after a mathematical principal, the fractals, which have a very specific structure with no "anomalies".

I don't think I am able to explain what fractals are in my own words, that's why I am going to include the definition from Wolfram Mathworld:

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox.

Illustrated above are the fractals known as the Gosper island, Koch snowflake, box fractal, Sierpiński sieve, Barnsley's fern, and Mandelbrot set.

  
When I first discovered fractals I was amazed to find that they exist everywhere in nature and manage to bring complexity to items that are actually rather simple.

The picture above describes the idea behind fractals, but if you want to learn (and understand more) you can check out the wikipedia page, or these two(1, 2) TED talks.

For this project I decided to combine two different yarns of the same weight, purchased from the same geographical area, but several years apart: the white one is a Russian wool/alpaca blend purchased in Riga, Latvia in late 2011 and the multicolor one a merino wool dyed and purchased from Turku, Finland in mid 2014.

They go well together and create a beautiful soft finish. The only issue here is that I run out of the multicolor yarn soon after the main color work was done (the skein was separated from the beginning into two halves and I wanted to use exactly one of the halves.), so I decided to continue working only with the white until it was all used up. That's why one part of the cowl is actually shorter that it should normally be. I used crochet to bind off all the stitches and at the same time create a set-up row for the crochet edge motif. In my eyes the result looks a bit weird, but OK nonetheless!

I finished it very late for winter (in May), but that was mostly because I didn't knit very often. A lot of things got in the way, I didn't have much motivation to knit, and it being a slow project didn't help at all!

But that doesn't mean that fractals and double-knitting won't come my way again! I have at least one crochet pattern in my queue that is a big fractal by itself!