Current approaches to characterize the complexity of dynamical systems usually rely on state-space trajectories. In this article instead we focus on causal structure, treating discrete dynamical systems as directed causal graphs—systems of elements implementing local update functions. This allows us to characterize the system’s intrinsic cause-effect structure by applying the mathematical and conceptual tools developed within the framework of integrated information theory (IIT). In particular, we assess the number of irreducible mechanisms (concepts) and the total amount of integrated conceptual information Φ
specified by a system. We analyze: (i) elementary cellular automata (ECA); and (ii) small, adaptive logic-gate networks (“animats”), similar to ECA in structure but evolving by interacting with an environment. We show that, in general, an integrated cause-effect structure with many concepts and high Φ
is likely to have high dynamical complexity. Importantly, while a dynamical analysis describes what is “happening” in a system from the extrinsic perspective of an observer, the analysis of its cause-effect structure reveals what a system “is” from its own intrinsic perspective, exposing its dynamical and evolutionary potential under many different scenarios.
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