By George Hart for the Museum of Mathematics

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Cellular automata are mathematical systems that can generate surprisingly complex patterns from very simple rules. Camilla Fox worked out a way to knit cellular automata patterns by using two colors of yarn. One of the two colors is brought to the front for each stitch according to a simple rule based on the colors of the three stitches in the row above it. The above image shows a tea cosy I commissioned from Fox based on the Rule 110 cellular automaton, which is mathematically interesting because it is proven to be Turing Complete.

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A second tea cosy, also following Rule 110, but with a different first row as its random initial condition, leads to a different instance in the same family of patterns.

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