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From 2014.igem.org

Pattern Formation Background

Cellular Automata

This pattern formation was formalized by Neuman in the concept of cellular automata. Following a simple pre-programmed logic rule, the state of a spot on the shell, corresponding to the color (either white or brown), is determined by the states of three parent spots (from the previous computation round). Wolfram ^[11] elaborated a whole theory on these cellular automata.

According to cellular automata theory, emergent patterns offer a large panel of properties: striking examples are the rule 30 which gives an apparently random pattern and the rule 110 which has been proven to be Turing complete. With cellular automata, you cannot predict how the final pattern will look like even if you know the rule that governs its property. Thus the intricated computations of steps poses the problem of complexity.

Logic Gate

We use the XOR logic gate on an hexagonal grid. It corresponds to the rule 6.