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Self-organization in micron-sized Nb3O7(OH) cubes during a hydrothermal treatment at 200 °C. Initially amorphous cubes gradually transform into ordered 3D meshes of crystalline nanowires as summarized in the model below.[1]

Self-organization is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process is spontaneous, not needing control by any external agent. It is often triggered by random fluctuations, amplified by positive feedback. The resulting organization is wholly decentralized, distributed over all the components of the system. As such, the organization is typically robust and able to survive or self-repair substantial perturbation. Chaos theory discusses self-organization in terms of islands of predictability in a sea of chaotic unpredictability.

Self-organization occurs in many physical, chemical, biological, robotic, social, and cognitive systems. Examples can be found in crystallization, thermal convection of fluids, chemical oscillation, animal swarming, and artificial and biological neural networks.


Self-organization is realized[2] in the physics of non-equilibrium processes, and in chemical reactions, where it is often described as self-assembly. The concept of self-organization has proven useful in the description of biological systems,[3] from the subcellular to the ecosystem level.[4] Cited examples of self-organizing behaviour also appear in the literature of many other disciplines, both in the natural sciences and in the social sciences such as economics or anthropology. Self-organization has also been observed in mathematical systems such as cellular automata.[5] Sometimes the notion of self-organization becomes conflated with that of the related concept of emergence.[6] Properly defined, however, there may be instances of self-organization without emergence and emergence without self-organization.[clarification needed (Example?)]

Self-organization usually relies on three basic ingredients:[7]

  1. strong dynamical non-linearity, often though not necessarily involving positive and negative feedback
  2. balance of exploitation and exploration
  3. multiple interactions

Principles of self-organization[edit]

The cybernetician William Ross Ashby formulated the original principle of self-organization in 1947.[8][9] It states that any deterministic dynamic system will automatically evolve towards a state of equilibrium that can be described in terms of an attractor in a basin of surrounding states. Once there, the further evolution of the system is constrained to remain in the attractor.[citation needed] This constraint on the system as a whole implies a form of mutual dependency or coordination between its constituent components or "subsystems". In Ashby's terms, each subsystem has adapted to the environment formed by all other subsystems.

The cybernetician Heinz von Foerster formulated the principle of "order from noise" in 1960.[10] It notes that self-organization is facilitated by random perturbations ("noise") that let the system explore a variety of states in its state space. This increases the chance that the system would arrive into the basin of a "strong" or "deep" attractor, from which it would then quickly enter the attractor itself. The thermodynamicist Ilya Prigogine formulated a similar principle as "order through fluctuations"[11] or "order out of chaos".[12] It is applied in the method of simulated annealing that is used[by whom?] in problem solving and in machine learning.


The idea that the dynamics of a system can lead to an increase in its organization has a long history. The ancient atomists believed that a designing intelligence is unnecessary to effect natural order, arguing that given enough time and space and matter, organization is ultimately inevitable, although there is no preferred tendency for this to happen.

The philosopher René Descartes presents it hypothetically in the fifth part of his Discourse on Method. He elaborated on the idea in his unpublished work The World.[a]

The economic concept of the "invisible hand" due to Adam Smith can be understood as an attempt to describe the influence of the market as a spontaneous order on people's actions.

Beginning with the 18th century, natural scientists sought to understand the "universal laws of form" in order to explain the observed forms of living organisms. Because of its association with Lamarckism, their ideas fell into disrepute until the early 20th century, when D'Arcy Wentworth Thompson attempted to revive them.

Sadi Carnot and Rudolf Clausius discovered the Second Law of Thermodynamics in the 19th century. It states that total entropy, sometimes understood as disorder, will always increase over time in an isolated system. This means that a system cannot spontaneously increase its order, without an external relationship that decreases order elsewhere in the system (e.g. through consuming the low-entropy energy of a battery and diffusing high-entropy heat).

The term "self-organizing" was used by Immanuel Kant in his Critique of Judgment, where he argued that teleology is a meaningful concept only if there exists such an entity whose parts or "organs" are simultaneously ends and means. Such a system of organs must be able to behave as if it has a mind of its own, that is, it is capable of governing itself.

The term "self-organizing" was introduced to contemporary science in 1947 by the psychiatrist and engineer W. Ross Ashby.[8] It was taken up by the cyberneticians Heinz von Foerster, Gordon Pask, Stafford Beer, and von Foerster organized a conference on "The Principles of Self-Organization" at the University of Illinois' Allerton Park in June, 1960 which led to a series of conferences on Self-Organizing Systems.[13] Norbert Wiener also took up the idea in the second edition of his Cybernetics: or Control and Communication in the Animal and the Machine (1961).

Self-organization as a word and concept was used by those associated with general systems theory in the 1960s, but did not become commonplace in the scientific literature until its adoption by physicists and researchers in the field of complex systems in the 1970s and 1980s.[14] After Ilya Prigogine's 1977 Nobel Prize, the thermodynamic concept of self-organization received some attention of the public, and scientific researchers started to migrate from the cybernetic view to the thermodynamic view.[15]



Convection cells in a gravity field

Examples from physics include:[citation needed]


The DNA structure at left (schematic shown) will self-assemble into the structure visualized by atomic force microscopy at right. Image from Strong.[18]

Self-organization in chemistry includes:

  1. molecular self-assembly
  2. reaction-diffusion systems and oscillating chemical reactions
  3. autocatalytic networks (see: autocatalytic set)
  4. liquid crystals
  5. grid complexes
  6. colloidal crystals
  7. self-assembled monolayers
  8. micelles
  9. microphase separation of block copolymers
  10. Langmuir-Blodgett films


Birds flocking, an example of self-organization in biology

According to Scott Camazine.. [et al.]:

Self-organization in biology can be observed in spontaneous folding of proteins and other biomacromolecules, formation of lipid bilayer membranes, homeostasis, pattern formation and morphogenesis in developmental biology, the coordination of human movement, social behaviour in insects (bees, ants, termites), and mammals, flocking behaviour in birds and fish, the origin of life itself.

Computer science[edit]

Gosper's Glider Gun creating "gliders" in the cellular automaton Conway's Game of Life.[20]

Phenomena from mathematics and computer science such as cellular automata, random graphs, and some instances of evolutionary computation and artificial life exhibit features of self-organization. In swarm robotics, self-organization is used to produce emergent behavior. In particular the theory of random graphs has been used as a justification for self-organization as a general principle of complex systems. In the field of multi-agent systems, understanding how to engineer systems that are capable of presenting self-organized behavior is a very active research area.


Many optimization algorithms can be considered as a self-organization system because the aim of the optimization is to find the optimal solution to a problem. If the solution is considered as a state of the iterative system, the optimal solution is essentially the selected, converged state or structure of the system, driven by the algorithm based on the system landscape.[21][22] In fact, one can view any optimization algorithm as a self-organizing system.


Only certain kinds of networks are self-organizing. The best known examples are small-world networks and scale-free networks. These emerge from bottom-up interactions, and appear to be limitless in size.[citation needed] In contrast, there are top-down hierarchical networks, which are not self-organizing. These are typical of organizations, and have severe size limits.[citation needed]

In many natural systems, self-organization results from repeated phase shifts in their underlying network of connections. Such phase shifts alter the balance between internal processes (e.g. selection and variation). They give rise to the phenomenon of dual-phase evolution.

Cloud computing systems have been argued to be inherently self-organising[23] and, while they exhibit autonomic features, are not self-managing as they do not have reducing complexity as a goal. Others argue that cloud computing represents a complex system and therefore self-organisation is an appropriate technique to address this complexity.[24][25] The European Union, through Horizon 2020, has recently funded CloudLightning, a Research Innovation Action. This project seeks to build a next generation cloud architecture based on the principles of decentralisation, self-organisation and self-management. Self organisation is used to manage complexity effectively and tackle the challenges of providing a Services Oriented Architecture that accommodates heterogeneous resources.


Norbert Wiener regarded the automatic serial identification of a black box and its subsequent reproduction as self-organization.[26] The importance of phase locking or the "attraction of frequencies", as he called it, is discussed in the 2nd edition of his "Cybernetics".[27] K. Eric Drexler sees self-replication as a key step in nano and universal assembly.

By contrast, the four concurrently connected galvanometers of W. Ross Ashby's Homeostat hunt, when perturbed, to converge on one of many possible stable states.[28] Ashby used his state counting measure of variety[29] to describe stable states and produced the "Good Regulator"[30] theorem which requires internal models for self-organized endurance and stability (e.g. Nyquist stability criterion).

Warren McCulloch proposed "Redundancy of Potential Command"[31] as characteristic of the organization of the brain and human nervous system and the necessary condition for self-organization.

Heinz von Foerster proposed Redundancy, R = 1 − H/Hmax, where H is entropy.[32][33] In essence this states that unused potential communication bandwidth is a measure of self-organization.

In the 1970s Stafford Beer considered this condition as necessary for autonomy which identifies self-organization in persisting and living systems. Using Variety analyses he applied his neurophysiologically derived recursive Viable System Model to management. It consists of five parts: the monitoring of performance of the survival processes (1), their management by recursive application of regulation (2), homeostatic operational control (3) and development (4) which produce maintenance of identity (5) under environmental perturbation. Focus is prioritized by an alerting "algedonic loop" feedback: a sensitivity to both pain and pleasure produced from under-performance or over-performance relative to a standard capability.[34]

In the 1990s Gordon Pask pointed out von Foerster's H and Hmax were not independent and interacted via countably infinite recursive concurrent spin processes[35] (he favoured the Bohm interpretation) which he called concepts (liberally defined in any medium, "productive and, incidentally reproductive"). His strict definition of concept "a procedure to bring about a relation"[36] permitted his theorem "Like concepts repel, unlike concepts attract"[37] to state a general spin-based principle of self-organization. His edict, an exclusion principle, "There are No Doppelgangers"[38][35] means no two concepts can be the same (all interactions occur with different perspectives making time incommensurable for actors).

Human society[edit]

Social self-organization in international drug routes

The self-organizing behaviour of social animals and the self-organization of simple mathematical structures both suggest that self-organization should be expected in human society. Tell-tale signs of self-organization are usually statistical properties shared with self-organizing physical systems (see Zipf's law, power law, Pareto principle). Examples such as critical mass, herd behaviour, groupthink and others, abound in sociology, economics, behavioral finance and anthropology.[39] The theory of human social self-organization is also known as spontaneous order theory.

In social theory the concept of self-referentiality has been introduced as a sociological application of self-organization theory by Niklas Luhmann (1984). For Luhmann the elements of a social system are self-producing communications, i.e. a communication produces further communications and hence a social system can reproduce itself as long as there is dynamic communication. For Luhmann human beings are sensors in the environment of the system. Luhmann developed an evolutionary theory of Society and its subsytems, using functional analyses and systems theory.[40]

Self-organization in human and computer networks can give rise to a decentralized, distributed, self-healing system, protecting the security of the actors in the network by limiting the scope of knowledge of the entire system held by each individual actor. The Underground Railroad is a good example of this sort of network. The networks that arise from drug trafficking exhibit similar self-organizing properties. The Sphere College Project seeks to apply self-organization to adult education. Parallel examples exist in the world of privacy-preserving computer networks such as Tor. In each case, the network as a whole exhibits distinctive synergistic behavior through the combination of the behaviors of individual actors in the network. Usually the growth of such networks is fueled by an ideology or sociological force that is adhered to or shared by all participants in the network.[original research?][15]


In economics, a market economy is sometimes said to be self-organizing. Paul Krugman has written on the role that market self-organization plays in the business cycle in his book "The Self Organizing Economy".[41] Friedrich Hayek coined the term catallaxy[42] to describe a "self-organizing system of voluntary co-operation", in regards to the spontaneous order of the free market economy. Neo-classical economists hold that imposing central planning usually makes the self-organized economic system less efficient. On the other end of the spectrum, economists consider that market failures are so significant that self-organization produces bad results and that the state should direct production and pricing. Most economists adopt an intermediate position and recommend a mixture of market economy and command economy characteristics (sometimes called a mixed economy). When applied to economics, the concept of self-organization can quickly become ideologically imbued.[15][43]

Collective intelligence[edit]

Visualization of links between pages on a wiki. This is an example of collective intelligence through collaborative editing.

Non-thermodynamic concepts of entropy and self-organization have been explored by many theorists. Cliff Joslyn and colleagues and their so-called "global brain" projects, Marvin Minsky's "Society of Mind", and the no-central editor in charge policy of the open sourced internet encyclopedia, called Wikipedia, are examples of applications of these principles – see collective intelligence.

Donella Meadows, who codified twelve leverage points that a self-organizing system could exploit to organize itself, was one of a school of theorists who saw human creativity as part of a general process of adapting human lifeways to the planet and taking humans out of conflict with natural processes. See Gaia philosophy, deep ecology, ecology movement and Green movement for similar self-organizing ideals. (The connections between self-organisation and Gaia theory and the environmental movement are explored in the book The Unity of Nature by Alan Marshall).

In learning[edit]

Enabling others to "learn how to learn"[44] is often taken to mean instructing them[45] how to submit to being taught. Self-organised learning (SOL)[46] denies that "the expert knows best" or that there is ever "the one best method", insisting instead on "the construction of personally significant, relevant and viable meaning"[47] to be tested experientially by the learner.[48] This may be collaborative, and more rewarding personally.[49][50] It is seen as a lifelong process, not limited to specific learning environments (home, school, university) or under the control of authorities such as parents and professors.[51] It needs to be tested, and intermittently revised, through the personal experience of the learner.[52] It need not be restricted by either consciousness or language.[53] Fritjof Capra argued that it is poorly recognised within psychology and education.[54] It may be related to cybernetics as it involves a negative feedback control loop,[36] or to systems theory.[55] It can be conducted as a learning conversation or dialogue between learners or within one person.[56][57]

Traffic flow[edit]

The self-organizing behavior of drivers in traffic flow determines almost all traffic spatiotemporal phenomena observed in real traffic data, such as traffic breakdown at a highway bottleneck, highway capacity, the emergence of moving traffic jams, etc. Self-organization in traffic flow is an extremely complex spatiotemporal dynamic process. For this reason, only in 1996–2002 did spatiotemporal self-organization effects in traffic become understood in real measured traffic data and explained by Boris Kerner's three-phase traffic theory.[citation needed]


In many complex systems in nature, there are global phenomena that are the irreducible result of local interactions between components whose individual study would not allow us to see the global properties of the whole combined system. Thus, a growing number of researchers think that many properties of language are not directly encoded by any of the components involved, but are the self-organized outcomes of the interactions of the components.

Building mathematical models in the context of research into language origins and the evolution of languages is enjoying growing popularity in the scientific community, because it is a crucial tool for studying the phenomena of language in relation to the complex interactions of its components. These systems are put to two main types of use: 1) they serve to evaluate the internal coherence of verbally expressed theories already proposed by clarifying all their hypotheses and verifying that they do indeed lead to the proposed conclusions ; 2) they serve to explore and generate new theories, which themselves often appear when one simply tries to build an artificial system reproducing the verbal behavior of humans.

As it were, the construction of operational models to test proposed hypotheses in linguistics is gaining much contemporary attention. An operational model is one which defines the set of its assumptions explicitly and above all shows how to calculate their consequences, that is, to prove that they lead to a certain set of conclusions.

In the emergence of language[edit]

Investigators have examined the emergence of language in the human species in a game-theoretic framework[58] based on a model of senders and receivers of information. The evolution of certain properties of language such as inference follow from this sort of framework (with the parameters stating that information transmitted can be partial or redundant, and the underlying assumption that the sender and receiver each want to take the action in their own best interest). Likewise, models have shown that compositionality, a central component of human language, emerges dynamically during linguistic evolution, and need not be introduced by biological evolution. Tomasello (1999) argues that one evolutionary step, the ability to sustain culture, laid the groundwork for the evolution of human language.[59][need quotation to verify]

In language acquisition[edit]

Within a species' ontogeny, the acquisition of language has also been shown to self-organize. Through the ability to see others as intentional agents (theory of mind), and actions such as 'joint attention,' human children have the scaffolding they need to learn the language of those around them.

In articulatory phonology[edit]

Articulatory phonology takes the approach that speech production consists of a coordinated series of gestures, called 'constellations,' which are themselves dynamical systems. In this theory, linguistic contrast comes from the distinction between such gestural units, which can be described on a low-dimensional level in the abstract. However, these structures are necessarily context-dependent in real-time production. Thus the context-dependence emerges naturally from the dynamical systems themselves. This statement is controversial, however, as it suggests a universal phonetics which is not evident across languages.[60] Cross-linguistic patterns show that what can be treated as the same gestural units produce different contextualised patterns in different languages.[61] Articulatory Phonology fails to attend to the acoustic output of the gestures themselves (meaning that many typological patterns remain unexplained).[62] Freedom among listeners in the weighting of perceptual cues in the acoustic signal has a more fundamental role to play in the emergence of structure.[63] The realization of the perceptual contrasts by means of articulatory movements means that articulatory considerations do play a role,[64] but these are purely secondary.

In diachrony and synchrony[edit]

Several mathematical models of language change rely on self-organizing or dynamical systems. Abrams and Strogatz (2003) produced a model of language change that focused on "language death" – the process by which a speech community merges into the surrounding speech communities. Nakamura et al. (2008) proposed a variant of this model that incorporates spatial dynamics into language contact transactions in order to describe the emergence of creoles. Both of these models proceed from the assumption that language change, like any self-organizing system, is a large-scale act or entity (in this case the creation or death of a language, or changes in its boundaries) that emerges from many actions on a micro-level. The microlevel in this example is the everyday production and comprehension of language by speakers in areas of language contact.


Heinz Pagels, in a balanced, but ultimately negative[citation needed] 1985 book review of Ilya Prigogine and Isabelle Stengers' Order Out of Chaos in Physics Today, appeals to authority:[65]

In theology, Thomas Aquinas (1225–1274) in his Summa Theologica assumes a teleological created universe in rejecting the idea that something can be a self-sufficient cause of its own organization:[66]

("The body of the Article" consists of the quinque viae.)

See also[edit]


  1. ^ Betzler, S. B.; Wisnet, A.; Breitbach, B.; Mitterbauer, C.; Weickert, J.; Schmidt-Mende, L.; Scheu, C. (2014). "Template-free synthesis of novel, highly-ordered 3D hierarchical Nb3O7(OH) superstructures with semiconductive and photoactive properties". Journal of Materials Chemistry A. 2 (30): 12005. doi:10.1039/C4TA02202E.  open access publication - free to read
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  5. ^ Ilachinski, Andrew (2001). Cellular Automata: A Discrete Universe. World Scientific. p. 247. ISBN 9789812381835. Retrieved 2016-04-05. We have already seen ample evidence for what is arguably the single most impressive general property of CA, namely their capacity for self-organization. 
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  28. ^ Ashby, William Ross (1952) Design for a Brain, Chapter 5 Chapman & Hall
  29. ^ Ashby, William Ross (1956) An Introduction to Cybernetics, Part Two Chapman & Hall
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  31. ^ Embodiments of Mind MIT Press (1965)"
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  34. ^ "Brain of the Firm" Alan Lane (1972) see also Viable System Model also in "Beyond Dispute " Wiley Stafford Beer 1994 "Redundancy of Potential Command" pp. 157–158.
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  40. ^ Luhmann, Niklas (1995) Social Systems. Stanford, California: Stanford University Press. ISBN 0804726256. p. 410.
  41. ^ Krugman, P. (1995) The Self Organizing Economy. Blackwell Publishers. ISBN 1557866996
  42. ^ Hayek, F. (1976) Law, Legislation and Liberty, Volume 2: The Mirage of Social Justice. University of Chicago Press.
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  44. ^ Rogers.C. (1969). Freedom to Learn. Merrill
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  58. ^ Compare: Jaeger, Herbert (2009). "What Can Mathematical, Computational, and Robotic Models Rell Us about the Origins of Syntax?". In Bickerton, Derek; Szathmáry, Eörs. Biological Foundations and Origin of Syntax. Strüngmann Forum reports. MIT Press. p. 393. ISBN 9780262013567. Possible applications of evolutionary game theory to the study of the cultural evolution of language [...] have been investigated 
  59. ^ Compare: Tomasello, Michael (2009-07-01) [1999]. The cultural origins of human cognition. Harvard University Press (published 2009). ISBN 9780674044371. 
  60. ^ Sole, M-J. (1992). "Phonetic and phonological processes: nasalization". Language & Speech. 35: 29–43. 
  61. ^ Ladefoged, Peter (2003) "Commentary: some thoughts on syllables – an old-fashioned interlude", pp. 269–276 in Papers in laboratory Phonology VI. Local, John, Richard Ogden & Ros Temple (eds.). Cambridge University Press.
  62. ^ see papers in Phonetica 49, 1992, special issue on Articulatory Phonology
  63. ^ Ohala, John J. (1996). "Speech perception is hearing sounds, not tongues". Journal of the Acoustical Society of America. 99 (3): 1718–1725. Bibcode:1996ASAJ...99.1718O. doi:10.1121/1.414696. PMID 8819861. 
  64. ^ Lindblom, B. (1999). Emergent phonology (PDF). Proceedings of the Twenty-fifth Annual Meeting of the Berkeley Linguistics Society, University of California, Berkeley. 
  65. ^ Pagels, H. R. (January 1, 1985). "Is the irreversibility we see a fundamental property of nature?" (PDF). Physics Today: 97–99. 
  66. ^ Article 3. Whether God exists?

Further reading[edit]

  • W. Ross Ashby (1966), Design for a Brain, Chapman & Hall, 2nd edition.
  • Amoroso, Richard (2005) The Fundamental Limit and Origin of Complexity in Biological Systems [1].
  • Per Bak (1996), How Nature Works: The Science of Self-Organized Criticality, Copernicus Books.
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