When conway meets wolfram: a study on life-like rules

Abstract

Cellular automata (CA) are simple, rule-based systems that can exhibit remarkably complex behavior. Among the most studied CA are Conway’s Game of Life (GoL) and Wolfram’s Elementary Cellular Automata (ECA), both of which have been widely explored for their emergent dynamics and computational potential. This thesis investigates the phenomenon of phase transitions in Life-like cellular automata—abrupt changes in macroscopic behavior—as a means to better understand the dynamics of complex systems and develop interpretable, CA-based pattern classifiers. The first contribution of this work is the generation of a labeled dataset that classifies whether Life-like rules exhibit phase transitions under three types of perturbation: α- asynchronous updates, spatial stochasticity, and temporal stochasticity. For each rule, a series of simulations was conducted across a parameter sweep (e.g., varying initial density), and transitions were detected based on changes in global density behavior. A total of over 35,000 rules were evaluated, with structured filtering and encoding to produce balanced datasets suitable for machine learning tasks. The second contribution is the design and evaluation of two asynchronous CA-based classifiers. The first, an attractor-based classifier inspired by previous work, failed to generalize reliably. The second, a novel classifier introduced in this thesis, uses a neural controller to guide the asynchronous evolution of encoded CA rules toward class-specific attractors. This NeuralACAClassifier demonstrated competitive accuracy (up to 84%) compared to standard machine learning baselines such as support vector machines, decision trees, and feedforward neural networks. Overall, this thesis presents a novel synthesis of complex systems theory and machine learning, showing that asynchronous CA are not only suitable for modeling emergent behaviors but can also serve as interpretable, lightweight classifiers of such behaviors.