Glossary
Cybernetics and complexity science are inherently multidisciplinary. Their ideas move between mathematics, physics, biology, computer science, social science, design, and other fields, often carrying slightly different meanings or emphases with them.
This glossary provides concise working introductions to core concepts and to established or emerging methods that appear across my research, teaching, and writing. It is not intended as an exhaustive dictionary. Rather, it offers a shared vocabulary for navigating the website and for seeing how ideas that originate in different disciplines can become connected.
How the ideas connect
Select a term to reveal neighbouring concepts that share one or more tags. The links indicate conceptual overlap rather than equivalence or a formal dependency.
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Adaptation A change in behaviour, structure, or organisation in response to conditions encountered over time.
In complex systems, adaptation may occur at the level of individual components, interactions, or the collective itself. The important question is often not simply whether a system changes, but what information it uses, what it retains from the past, and what remains stable while it changes.
Agent-based modelling A computational approach that represents individual agents and their local rules to study collective behaviour.
Rather than prescribing a system's large-scale behaviour directly, an agent-based model specifies how individual entities act and interact. Repeated simulation then reveals what macroscopic patterns, regularities, or unexpected behaviours can emerge from those rules.
Allostasis The maintenance of stability through change, including adaptive and anticipatory regulation.
Allostasis shifts attention away from returning to one fixed state and towards maintaining viability as conditions change. On this website, the idea is particularly useful for thinking about systems that respond to current conditions while also anticipating what may happen next.
Attractor A state or set of states towards which a dynamical system tends to evolve after transient behaviour.
Attractors provide one way of describing the long-term organisation of dynamics. Depending on the system, an attractor may be a fixed point, a repeating cycle, or a more complicated set of states.
Complexity science The study of systems whose collective behaviour arises from many interacting components and cannot be understood from the components alone.
Complexity science asks how interactions, feedback, heterogeneity, adaptation, and history produce organisation across scales. Its methods span analytical models, simulation, network analysis, statistical physics, data-driven approaches, and qualitative inquiry.
Criticality Behaviour associated with the vicinity of a transition where fluctuations and correlations can extend across many scales.
Near a critical point, systems can become unusually sensitive to perturbations and may display scaling behaviour or long-range correlations. The concept originates in statistical physics but has also inspired broader approaches to biological, computational, and social systems.
Cybernetics A transdisciplinary field concerned with communication, feedback, control, regulation, and purposeful behaviour in systems.
Cybernetics studies how systems sense, communicate, act, and regulate themselves or one another. Rather than belonging to one application domain, its concepts have travelled across engineering, biology, cognition, organisations, design, and social systems.
Emergence The appearance of collective patterns or properties that arise from interactions among components.
An emergent pattern need not be explicitly represented in the rules followed by individual components. The concept is therefore central to understanding how simple local interactions can produce organised behaviour at a larger scale.
Feedback A process in which the consequences of an action or state influence what the system does next.
Feedback can stabilise, amplify, or reorganise behaviour depending on how information is returned and acted upon. It is a foundational concept in cybernetics and a recurring mechanism across biological, technological, ecological, and social systems.
Feedforward Anticipatory action taken in response to an expected change rather than only to an observed error.
Where feedback responds to consequences that are already observable, feedforward uses a model, cue, or expectation about what is likely to happen. The distinction is useful when studying adaptive systems that combine reaction with anticipation.
Hyperuniformity A form of large-scale order characterised by unusually suppressed long-wavelength density fluctuations.
Hyperuniform systems can be disordered at short distances while becoming strongly constrained at large scales. This makes hyperuniformity useful for studying forms of order that lie between conventional categories such as crystals and ordinary disordered materials.
Persistent homology A topological data analysis method that tracks features such as connected components and loops across scale.
Instead of choosing one scale in advance, persistent homology asks when topological features appear and disappear as a scale parameter changes. Features that persist across a wide range of scales are often interpreted as more structurally significant than short-lived ones. Try this interactive demo to get a sense of how persistent homology works.
Phase transition A qualitative change in a system's collective state that occurs when a control parameter crosses a threshold.
A phase transition occurs when a system changes from one macroscopic state or regime to another as some condition is varied. Familiar physical examples include water freezing into ice or a magnet losing its magnetisation as temperature changes. In complex systems, the idea is used more broadly to describe abrupt or qualitative changes in collective organisation, behaviour, or connectivity.
Near a transition point, small changes in local interactions can sometimes produce large-scale changes across the whole system. This makes phase transitions closely related to ideas such as criticality, emergence, collective behaviour, and scaling.
Scaling A relationship in which the behaviour or structure of a system changes systematically with scale, often following simple mathematical laws.
Scaling describes how a quantity changes as the size, resolution, distance, time scale, or some other characteristic scale of a system is varied. In many complex systems, these relationships can be expressed through power laws, where the same mathematical form persists across a range of scales.
Scaling is closely associated with criticality and phase transitions, where systems may develop correlations across many different length or time scales and lose a single characteristic scale. Similar scaling behaviour can sometimes appear in otherwise very different systems, which is one reason the concept is also closely connected to universality.
Self-organisation The formation or maintenance of collective organisation through local interactions without a central controller specifying the global pattern.
Self-organisation does not imply the absence of constraints, environments, or external influences. It describes how coordination at one scale can arise through interactions occurring at another.
Topology The mathematics of qualitative structure, including properties such as connectivity and holes that persist under continuous deformation.
Topology provides a language for describing structure without depending on exact distances or angles. In data analysis, this perspective can help identify robust organisation that may be difficult to see using purely metric or coordinate-based descriptions.
Universality The appearance of the same large-scale behaviour in systems whose microscopic details can be very different.
Universality is especially important in the theory of critical phenomena, where systems with different constituents can share the same scaling laws. More broadly, it motivates the search for structural principles that survive changes in microscopic implementation.
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