Complexity and information: Measuring emergence, self-organization, and homeostasis at multiple scales
Open accessAbstract
Abstract Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this article, we use information theory to provide abstract and concise measures of complexity, emergence, self‐organization, and homeostasis. The purpose is to clarify the meaning of these concepts with the aid of the proposed formal measures. In a simplified version of the measures (focusing on the information produced by a system), emergence becomes the opposite of self‐organization, while complexity represents their balance. Homeostasis can be seen as a measure of the stability of the system. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales. © 2012 Wiley Periodicals, Inc. Complexity, 2012
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
This approach allows us to evaluate the axioms underlying the measures, as opposed to trying to compare different measures without a common ground.
“Having in mind that there are several different measures already proposed (Prokopenko et al., 2009; Gershenson and Fern´ andez, 2012), this approach allows us to evaluate the axioms underlying the measures, as opposed to trying to compare different measures without a common ground.”
From Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis (2013) · cites this paper as Gershenson and Fern´ andez, 2012
Cites
Self-Organization in Biological Systems
Sneyd, J., Theraula, G., Bonabeau, E., Deneubourg, J.-L., & Franks, N. R. (2001) · doi:10.1515/9780691212920 · Cited by 2,949 · see citing works
Computation at the edge of chaos: Phase transitions and emergent computation
Langton, C. G. (1990) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(90)90064-v · Cited by 1,527 · see citing works
Relating Fisher information to order parameters.
Prokopenko, M., Lizier, J. T., Obst, O., & Wang, X. R. (2011) · Physical Review E · doi:10.1103/physreve.84.041116 · Cited by 122 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Information Measures of Complexity, Emergence, Self-organization, Homeostasis, and Autopoiesis
Fernandez, N., Maldonado, C., & Gershenson, C. (2013) · arXiv · doi:10.48550/arxiv.1304.1842 · Cited by 1 · see citing works
“Having in mind that there are several different measures already proposed (Prokopenko et al., 2009; Gershenson and Fernández, 2012), this approach allows us to evaluate the axioms underlying the measures, as opposed to trying to compare different measures without a common ground.”
BackgroundMethodResultInfluentialSelf-citation
- Authors
- Gershenson, C., & Fernández, N.
- Affiliations
- Universidad Nacional Autónoma de México (MX)
- Universidad de Los Andes (VE)
- Corresponding author
- Gershenson, Carlos
- ORCID
- Gershenson, Carlos
- Venue
- Complexity
- Publisher
- Wiley
- Published
- 2012-09-24
- Volume
- 18
- Issue
- 2
- Pages
- 29-44
- ISSN
- 1076-2787 (ISSN-L)
- 1099-0526
- OpenAlex
- W2143902672
- Cited by
- 179
- References
- 3
- Citations by year
- 2026: 4 · 2025: 8 · 2024: 10 · 2023: 14 · 2022: 10 · 2021: 13 · 2020: 19 · 2019: 21 · 2018: 18 · 2017: 12 · 2016: 15 · 2015: 9 · 2014: 14 · 2013: 9 · 2012: 3
- FWCI
- 8.49
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Complexity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Consejo Nacional de Ciencia y Tecnología
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Chaos, Complexity, and Education
- Keywords
- complexity measures, emergence, self-organization, homeostasis, information theory, information production, system stability, random Boolean networks, elementary cellular automata, multiscale analysis, complex systems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
