Is Life Alone in the Universe of Symmetric Cellular Automata?
Iñaki Minondo and Clifford A. Reiter
We investigate computational methods for seeking complex behavior among 2-dimensional Boolean automata.We consider general automata and those that respect various symmetries on local 3 by 3 Moore neighborhoods. We use the standard deviation of input entropy to guide Monte Carlo searches. We also use genetic algorithms for finding complex automata from other complex automata. We also use searches that require the simple glider that arises in Life to be viable and do likewise for other simple gliders that arise in general symmetric searches. Indeed, our richest searches for complex automata utilized symmetry, required very simple gliders to be viable, and used bounds on input entropy in Monte Carlo searches. While complex behavior may be rare in rule-space, it appears that there are many symmetric cellular automata with complex behavior that can be found using the techniques that we discuss.
Keywords: Symmetric cellular automata, complex behavior, self-organizing, gliders