Non-equilibrium dynamics of classical cellular automata

This research investigates classical cellular automata (CA) as models for complex many-body systems through their non-equilibrium dynamics. In this thesis we study the development of ordered patterns and phase transitions through basic local deterministic rules by observing their evolution from random initial states. The research begins with an analysis of one-dimensional elementary CA by studying their statistical characteristics when run under synchronous and asynchronous update protocols. We focuses on Conway's Game of Life, two-dimensional CA system by using initial live cell density as a control parameter to analyze its long-term outcomes. The simulations reveal two distinct non-equilibrium phase transitions that separate a dynamic phase from two inactive ones: a low-density absorbing ``dead” state and a high-density frozen ``static” state. These findings show that even simple deterministic CA can generate rich phase diagrams, providing valuable insights into self-organization and critical phenomena outside thermal equilibrium.‎