Chaotic knitting

An interesting way to knit!

Botanica Mathematica

In mathematics, a chaotic system is one which has clear rules on what to do from one time step to the next, but where the outcome is unpredictable because it is so sensitive to the starting conditions.  Amazingly, we can make up a very simple knitting pattern which is complete chaos…

Let me give you the general idea before I get into specifics. There are two colours. You start with a row consisting of the colours chosen in a random order. Then in subsequent rows, the colour of a stitch depends on the colours of the three stitches below it. (That is, the one directly below and the ones either side of that stitch.) If you’re at an edge stitch, you need to look at the stitches at the other end of the row – imagine they wrap around in a circle.

The specific rule I chose is the following…

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