LQ placeholderSurprising results of simple rules

Surprising results of simple rules

Understanding complex dynamical behaviours generated by simple rules, such as cellular automata, polyominoes and models of aggregation.

Background Most simple rules give rise to simple behaviours. But occasionally they generate surprisingly rich and varied dynamics. Some simple rules, such as Conway’s game of life, are even capable of universal computation. While applying simple rules is easy, deducing the rules from observed behaviour is both important and usually hard, as evidenced by the deduction of the laws of physics through science.

Project We investigate different classes of simple rules for discrete dynamics. We help classify elementary cellular automata by deducing general characteristics of their behaviour. We study the self-assembly of polyominoes and the reverse engineering of structures made from them. In simple models of competition, mathematical models help us track the long-term fitness of the population.

Consequences Reverse engineering simple rules that generate desired dynamics can help us design efficient algorithms and low-cost methods of assembly. Understanding of which rules give rise to behaviour that is not fully stable nor entirely chaotic may help design systems for artificial life and synthetic biology.

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