Gliders and Riders: A Particle Swarm Selects for Coherent Space-Time Structures in Evolving Cellular Automata

Abstract

Cellular Automata (CA) which are capable of universal computation exhibit complex dynamics, and they generate gliders: coherent space-time structures that “move” information quanta through the CA lattice. The technique described here is able to evolve CA transition functions that generate glider-rich dynamics. Patternrecognition algorithms for detecting gliders can be used as a way to determine the relative fitness among a population of CA rules, for use in a genetic algorithm (GA). However, digital image-based techniques for this purpose can be computationally expensive. In contrast, this technique is inspired by particle swarm optimization: the particles guide evolution within a single, heterogeneous 2D CA lattice having unique, evolvable transitions rules at each site. The particles reward local areas which give them a “good ride”, by performing genetic operators on the CA’s transition functions while the CA is evolving. It is shown that the resulting dynamics converge numerically to the edge of chaos, using a measure of the lambda value. This technique is not only efficient in evolving glider-rich CA of great variety, but it also models a kind of symbiosis: the swarm and the CA dynamics engage in a mutual evolutionary dance. Using a swarm to evolve gliders places the search for universal CA into a new context. A proposal for detecting types of glider collisions, aided by swarm communication, is offered, which could be used as a tool to better understand emergent computation.