Distinct Regimes of Predictive Accessibility in Elementary Cellular Automata
Rodrigo A. Garrido
Faculty of Engineering & Sciences
Universidad Adolfo Ibáñez
Av. Diagonal Las Torres 2700, Peñalolén
Santiago, RM, Chile
Abstract
Predicting the evolution of deterministic dynamical systems is often treated as a problem of model capacity, architecture design or training procedure. However, in local dynamical systems, long-term predictability may be constrained not only by the expressivity of the predictor, but also by the way dynamically relevant information propagates, disperses and remains accessible under finite learned representations. In this paper, we investigate this issue using elementary cellular automata (ECAs) as a minimal setting in which local deterministic rules generate qualitatively different global dynamics. Rather than framing prediction failure as a generic limitation of machine learning models, we study the emergence of distinct regimes of predictive accessibility: the extent to which information relevant for future states can be captured and exploited by finite learned representations under a given observational framework. Using neural predictors with controlled receptive fields, we show that different cellular automaton rules exhibit qualitatively different forms of predictive behavior. Rule 30 displays an abrupt loss of accessible predictive structure beyond a receptive-field-dependent horizon. Rule 45 exhibits a smoother degradation regime. Rule 90, despite being deterministic and linear over , remains near chance-level performance under the tested representations, consistent with distributed XOR-like dependencies that are difficult to compress statistically. Rule 110, by contrast, retains substantial predictive structure over longer horizons, suggesting that complex dynamics need not imply immediate loss of predictability. These results indicate that prediction limits in ECAs are not adequately described as a uniform consequence of error accumulation or insufficient model capacity. Instead, they reflect rule-dependent differences in information structure, causal accessibility and statistical compressibility. The proposed framework reframes predictability as an empirical property of the interaction between dynamics and representation, rather than as a purely algorithmic capability.
Keywords: elementary cellular automata; predictive accessibility; dynamical systems; machine learning; information propagation; statistical compressibility
Cite this publication as:
R. A. Garrido, “Distinct Regimes of Predictive Accessibility in Elementary Cellular Automata,” Complex Systems, 35(3), 2026 pp. 267–298.
https://doi.org/10.25088/ComplexSystems.35.3.267
