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Entropy 2015, 17(8), 5472-5502; doi:10.3390/e17085472

The Intrinsic Cause-Effect Power of Discrete Dynamical Systems—From Elementary Cellular Automata to Adapting Animats

Department of Psychiatry, University of Wisconsin, Madison 53719, WI, USA
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Authors to whom correspondence should be addressed.
Academic Editors: Christoph Salge, Georg Martius, Keyan Ghazi-Zahedi and Daniel Polani
Received: 22 May 2015 / Revised: 20 July 2015 / Accepted: 28 July 2015 / Published: 31 July 2015
(This article belongs to the Special Issue Information Theoretic Incentives for Cognitive Systems)
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Abstract

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. View Full-Text
Keywords: integration; information; causation; artificial evolution integration; information; causation; artificial evolution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Albantakis, L.; Tononi, G. The Intrinsic Cause-Effect Power of Discrete Dynamical Systems—From Elementary Cellular Automata to Adapting Animats. Entropy 2015, 17, 5472-5502.

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