# Surprising results of simple rules

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

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

S. Ahnert, I. Johnston, T. Fink, J. Doye, A. Louis

*Physical Review E*

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 equivalent to a universal Turing machine and can compute any computable function. 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.

In this project we investigate different families 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 behaviour of a population.

Reverse engineering simple rules that generate desired behaviour can help us design efficient algorithms and low-cost methods for manufacturing. Understanding which rules give rise to dynamics that are neither fully stable nor entirely chaotic may help design systems for artificial life and synthetic biology.

S. Ahnert, I. Johnston, T. Fink, J. Doye, A. Louis

*Physical Review E*