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1Clear out junk files and repair common Windows errors2Fix the driver behind crashes, sound loss and screen glitches3Repair Windows errors before they cause bigger problemsEmergence is what happens when many interacting parts produce a pattern or property that none of them carries alone. A flock turns as one body although no bird leads it. Water becomes ice, a lattice no single molecule forms. The idea is simple to state. Predicting and steering the outcomes it produces is where the difficulty begins, and that difficulty varies a great deal from one system to another.
A working definition of emergence
For practical use, emergence occurs when coherent system-level properties or patterns arise dynamically from interactions among lower-level components, and cannot be attributed to any one component in isolation. That definition is a working tool, not a settled theory.
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Two definitions reproduced in a 2025 review in Frontiers in Complex Systems (“Emergence as a science”) show how the concept is usually framed. The first, from De Wolf and Holvoet, reads: “A system exhibits emergence when there are coherent emergents at the macro-level that dynamically arise from the interactions between the parts at the micro-level. Such emergents are novel with regard to the individual parts of the system.” The second, from Goldstein, reads: “Emergence is the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems.”
Both definitions cover process and outcome. The De Wolf and Holvoet version stresses novelty relative to the parts. The Goldstein version stresses self-organization. Writers who use the word should say which of these criteria they mean, because a pattern can satisfy one without clearly satisfying the other.
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Where the definitions disagree
The disagreement is real and should be stated rather than smoothed over. The Frontiers review says several definitions remain acceptable given the range of phenomena that get called emergent. The UK Government’s Magenta Book supplementary guide, Handling complexity in policy evaluation, says there is no single agreed definition of complexity. A chapter from the National Academies Press, Robert M. Hazen’s “The Missing Law” in Genesis: The Scientific Quest for Life’s Origin (2005), states that a rigorous definition and a precise mathematical formulation of emergence remain elusive.
In practice, this means a claim that something is “emergent” is only as clear as the definition behind it. Name the criterion, name the level at which the pattern appears, and say what evidence supports it.
Components versus relations
The most useful distinction for readers is between components and relations. Knowing what the parts are does not tell you what the whole will do. A 2020 review in Complexity (Wiley), “An Introduction to Complex Systems Science and Its Applications,” makes this point with water. Steam and ice are both made of water molecules, yet they have very different properties, because the interactions among molecules differ in each case.
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Repair Windows errors before they cause bigger problemsFix Now →Fix the driver behind crashes, sound loss and screen glitchesFind Drivers →The same logic applies to turbulence, flocking, and spontaneous social grouping. In each, a large-scale pattern is produced by how elements relate to one another, not by a property stored in any single element. Changing the relations, while keeping the parts the same, changes the pattern.
How interactions produce system-level patterns
Several mechanisms recur across the examples. They rarely act alone, and each one changes how far the outcome can be predicted.
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Local interaction without central control
Many emergent patterns arise when each component responds only to its neighbours or to a few signals, with no coordinator. The 2020 review defines self-organization as patterns arising without external or centralized control, from interactions among components. Self-organization is a narrower idea than emergence in general. Many self-organized patterns are emergent, but the two terms should not be treated as identical.
Nonlinear and non-proportional interaction
When a small change in one part produces an effect far larger or smaller than expected, outcomes stop scaling with inputs. The UK guide lists non-linear and non-proportional interaction as a characteristic of complex adaptive systems. This is why doubling an input does not necessarily double an output, and why a system can look stable until it suddenly does not.
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Feedback
Feedback occurs when the output of an interaction changes the conditions that produced it. Positive feedback can amplify a pattern; negative feedback can hold it in place. Feedback is one of the main reasons a system’s behaviour is hard to read from its parts: the same interaction can reinforce or suppress itself depending on where the system currently sits.
Adaptation and learning
Components that change their behaviour in response to outcomes make the system harder to predict, because the rules themselves shift. The UK guide gives an example of targets prompting people or organisations to game a measure. The intervention changes what people do, and the measure stops reflecting what it was meant to track.
Environmental coupling
External conditions, such as temperature, pressure, resources, or regulation, shape which patterns are possible. The same internal interactions can produce different system-level behaviour under different environments.
Examples, and what each one does and does not show
Examples are most useful when they are paired with their limits. The sources reviewed use the following cases, and each illustrates a different point.
Phase behaviour
The collective behaviour that distinguishes solids, liquids, and gases is treated as emergent in the 2020 review. It shows clearly that a whole’s properties cannot be read off a single molecule. It does not, by itself, show how to predict every phase transition in every material.
Fluid turbulence
Large-scale turbulent motion can arise through relations among fluid elements, with no central controller directing it. This is a standard example of pattern arising from interaction, though turbulence is also notoriously hard to predict in detail.
Bird flocking
Flocking is a familiar self-organized pattern. The National Academies Press chapter discusses Craig Reynolds’s BOIDS simulation, which reproduces collective, animal-like movement from a few simple instructions. A simulation that reproduces the visible pattern shows that simple local rules are sufficient to generate it. It does not, on its own, establish that real birds follow those same rules.
Queues, conversation groups, and social norms
The reviewed sources list conversation groups, queues, social norms, social movements, and new markets as group-level patterns. A queue is a useful everyday example, because nobody designs its shape in advance. Even so, these cases should not be lumped together as having one mechanism. A queue forms through individual decisions about where to stand. A market forms through prices, information, and expectations. The label covers both, but the drivers differ.
Ecological resilience
The Magenta Book identifies an ecosystem’s resilience to external change as an emergent property of interactions among species. Resilience is a whole-system property. No single species carries it.
Brain and networks
The University of Michigan Center for the Study of Complex Systems lists cognition in the brain and the robustness of networks among its emergent functionalities. These are real and important examples. They are not, however, settled explanations of how those functions arise in detail, and they should be presented as examples rather than as completed accounts.
The depth we didn’t design
The phrase points to a practical problem. Designers and observers can specify components and interfaces, but they usually cannot list every system-level effect that will come out of how those parts interact. The Systems Engineering Body of Knowledge (SEBoK), in its “Emergence and Complexity” entry, states that modern engineered systems operate in complex socio-technical environments and may not be completely predictable during design. Some emergent behaviour becomes understandable only through operational experience.
SEBoK recommends a set of practices in response: architecture and modularization, interface management, modeling and simulation, iteration and experimentation, prototyping, stakeholder engagement, and operational monitoring and adaptation. None of these removes emergence. They shorten the distance between what designers expected and what the system actually does.
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Desirable emergence as well as harmful emergence
Emergence is not inherently accidental or undesirable. SEBoK notes that desirable system properties, including resilience, safety, adaptability, usability, and mission effectiveness, exist at the whole-system level. The engineering challenge it describes is to increase the likelihood of desirable emergence while reducing the likelihood and impact of harmful or unexpected emergence. The same interactions that make a system robust can, under other conditions, make it fragile, so the question is which relations to strengthen and which to constrain.
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Can emergent behaviour be predicted?
Predictability is not a yes-or-no property. SEBoK describes simple emergence, in which system-level properties are predictable because the elements and their relationships are well understood. It also distinguishes more complex forms, and cautions that some behaviours may only be understood operationally. Use the following axes to place a given example along that range.
| Axis | Question to ask | What tends to make prediction harder |
|---|---|---|
| Scale | What is the component level, and what is the system level being described? | A large gap between the two, with many intermediate levels in between |
| Interaction pattern | Are relations linear or nonlinear, local or networked, independent or mutually influential? | Nonlinear, networked, and mutually influential relations |
| Feedback and adaptation | Do components respond to outcomes, learn, or change their own behaviour? | Components that change their rules in response to the system’s outcomes |
| Environmental coupling | How strongly do external conditions shape the pattern? | Strong dependence on conditions that shift over time |
| Predictability and evidence | Can established theory predict the behaviour, or is modeling, simulation, experimentation, or operational learning needed? | No validated model, so only testing and observation can establish behaviour |
When modeling works and when it does not
Where the elements and their relationships are well understood, modeling can predict system-level behaviour with reasonable confidence. Where they are not, simulation can explore possibilities, and iterative testing and operational monitoring can establish what actually happens. The reviewed sources do not treat these as competing approaches. They are used at different stages, and the choice depends on how much of the system’s logic is already known.
Complex interventions
Policy and programme design show the limits of advance prediction clearly. Patricia Rogers, quoted in the Magenta Book supplementary guide, says: “it is complex interventions that present the greatest challenge for evaluation and for the utilization of evaluation, because the path to success is so variable and it cannot be articulated in advance.” The passage does not establish her professional role, so the quotation is cited here without a title.
Intervening in systems that adapt
An intervention in a system whose components adapt is itself part of the system. Once a measure becomes a target, the people being measured may adjust to it, as the Magenta Book’s gaming example shows. Plans for intervention should therefore assume that the system will respond, and should include ways to check whether the measure still tracks what it was meant to track. Changes should be introduced in stages where possible, so that unexpected responses appear while they are still small enough to correct.
Attention to relations is the design implication that runs through each of these sections. Whole-system properties, desirable and harmful, depend on how parts interact, and the parts list alone will not show them.
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