{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T13:04:21Z","timestamp":1774357461885,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2015,7,31]],"date-time":"2015-07-31T00:00:00Z","timestamp":1438300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Templeton World Charities Foundation","award":["#TWCF 0067\/AB41"],"award-info":[{"award-number":["#TWCF 0067\/AB41"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2014systems of elements implementing local update functions. This allows us to characterize the system\u2019s 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 \u03a6 specified by a system. We analyze: (i) elementary cellular automata (ECA); and (ii) small, adaptive logic-gate networks (\u201canimats\u201d), 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 \u03a6 is likely to have high dynamical complexity. Importantly, while a dynamical analysis describes what is \u201chappening\u201d in a system from the extrinsic perspective of an observer, the analysis of its cause-effect structure reveals what a system \u201cis\u201d from its own intrinsic perspective, exposing its dynamical and evolutionary potential under many different scenarios.<\/jats:p>","DOI":"10.3390\/e17085472","type":"journal-article","created":{"date-parts":[[2015,7,31]],"date-time":"2015-07-31T10:12:24Z","timestamp":1438337544000},"page":"5472-5502","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":48,"title":["The Intrinsic Cause-Effect Power of Discrete Dynamical Systems\u2014From Elementary Cellular Automata to  Adapting Animats"],"prefix":"10.3390","volume":"17","author":[{"given":"Larissa","family":"Albantakis","sequence":"first","affiliation":[{"name":"Department of Psychiatry, University of Wisconsin, Madison 53719, WI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giulio","family":"Tononi","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, University of Wisconsin, Madison 53719, WI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,7,31]]},"reference":[{"key":"ref_1","unstructured":"Nykamp, D. 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