Toward Automated Identification of Turing-Complete Cellular Automata via Structural and Complexity Analysis

This research presents a unified, quantitative framework for analyzing the complexity and computational potential of Cellular Automata (CA). By combining the Complexity Score (CS) with the Behavioral Index (BI), the method systematically identifies rules that generate both complex structures and non-trivial interactions - features that recur across known constructions of Turing-complete systems and motivate their use as practical search criteria. This methodology provides a reproducible approach to estimating unbiased simulation parameters, ensuring robust measurements regardless of grid size, time step, or random seed. This reduces variability and enhances comparability across different CA rules and dimensions. The framework applies to all N-dimensional CAs, highlighting edge-of-chaos characteristics. Behavioral analysis allows detailed tracking of object dynamics and collision interactions, providing insights that are not captured by structural metrics alone. Overall, this approach lays a foundation for scalable, quantitative exploration of CA rule spaces and for the systematic identification of candidate universal automata, enabling efficient studies in this area and advancing practical uses of CAs.