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Complex Systems Glossary


In this glossary each entry is an hypertext link that takes you to an introduction describing that concept in a wider context. Alternatively, to read all the introductions in sequence start with "Setting The Scene". This is a brief glossary, for a more detailed one see: ISAAC's. Some of the terms included here are specific to the wider CALResCo viewpoint and may not be common in the work of other more specialised groups.
The ability of an organism to learn in response to changes in its environment over the course of its lifetime. This allows it to improve its fitness over that available from its initial phenotype.
The ability of a species to change in response to changes in its environment over many generations. This requires changes to the genotype in a way that increases an individuals' fitness.
Individuals within an interacting population, each may have only limited freedom to react to their neighbours yet the behaviour of the whole (emergent) may be much more complex. Collections of agents are sometimes called 'swarms'. Agent-based models (ABMs) are central to complexity research.
A collection of parts brought together without interactions, typical of the reductionist approach which ignores emergent effects and self-organisation.
Abbreviation for Artificial Life, the study of alternative forms of life to biological (BLife), also abbreviated to AL in contrast with AI (artificial intelligence) which concentrates on the emulation of psychological behaviours.
A point to which a system tends to move, a goal, either deliberate or constrained by system parameters (laws). The three standard attractor types are fixed point, cyclic and strange (or chaotic).
Arms Race
Two species changing in response to changes in the other, a typical predator - prey interaction. This is usually regarded as a negative-sum interaction, improvements cancel each other out.
A process that creates itself by catalytic action. A system of chemical reactions such that each reaction is aided (catalysed) by the product of another in a closed and self-perpetuating sequence.
A form of system that can act independently, e.g. a robot. Used in complexity to refer to active (teleological) agents rather than passive ones, i.e. agents with internal goals that can act differently in identical external circumstances.
Self-production or self-maintenance. The ability to maintain a bounded form despite a flow of material occurring. A non-equilibrium system, typically life or similar processes but in a wider sense also including natural phenomena like Jupiter's Red Spot. See also sympoietic.
Aware Systems
Systems that can respond to their environment in an autonomous way, detecting external conditions and reacting appropriately (a teleological drive). Systems that can plan ahead, also called anticipatory systems.
The study of values and their types. These can be of four types, systemic, extrinsic, intrinsic and holarchic. Complex systems are of the latter two types.
Basin of Attraction
The set of initial states which are drawn to an attractor of the system.
A point at which a system splits into two alternative behaviours, either being possible, the one actually followed often being indeterminate (unpredictable). Related to catastrophes in Catastrophe Theory.
Boolean Network
A combination of interconnected logic gates often used to model complex phenomena and demonstrating the emergence of multiple attractors in simple systems.
Butterfly Effect
The possibility that a large change can occur from a minor shift in initial conditions. A butterfly flapping its wings in the Amazon leading to changes in the location of a typhoon elsewhere in the world. Sensitivity to initial conditions, a chaotic system.
The restriction of state space exploration by constraints imposed upon the system either from outside or self-generated, i.e. unavailable possibilities. This helps to preserve stability or the 'status-quo' but may also prevent better optima from being reached.
A reaction taking place due to the presence of an enabling agent, one that is not changed in the process. An essential part of autocatalytic processes.
Cellular Automata (CA)
Simple agents that have a limited number of states, arranged in a grid formation. The state occupied is solely determined by the agent states together with those of their immediate surroundings. The cells in the 'Game of Life' are of this type.
A system whose long term behaviour is unpredictable, tiny changes in the accuracy of the starting value rapidly diverge to anywhere in its possible state space. There can however be a finite number of available states, so statistical prediction can still be useful.
Circular Causation
The formation of closed loops of cause and effect within the system, such that it is not possible to abstract a linear chain of explanation in the conventional manner. A feature of all complex systems, which typically incorporate many such loops and exhibit multiple interconnected causes and effects.
A set of production rules used to match environmental data and suggest an action to be taken, usually incorporates a genetic algorithm. Each rule covers part of state space.
Evolution of species, not only with respect to their environment, but also as to how they relate to other species. This is a more potent form of evolution to that normally considered, changing the shape of the fitness landscape dynamically.
The idea that to survive agents must fight each other and that only one of them can be successful. This assumes that resources are limited (insufficient for both) and is often a negative-sum strategy, i.e. 'win-lose' or 'lose-lose'.
Complex Adaptive System
A form of system containing many autonomous agents who self-organize in a coevolutionary way to optimise their separate values.
The interaction of many parts, giving rise to difficulties in linear or reductionist analysis due to the nonlinearity of the inherent circular causation and feedback effects.
Complexity Philosophy
A set of organic axioms or assumptions more appropriate to nonlinear and interacting complex systems.
Complexity Science
The study of the rules governing emergence, the constraints affecting self-organisation and general system dynamics in nonlinear adaptive interacting systems. The study of the collective behaviour of macroscopic collections of interacting units that are endowed with the potential to evolve in time.
Complex System
One not describable by a single rule. Structure exists on many scales whose characteristics are not reducible to only one level of description. Systems that exhibit unexpected features not contained within their specification. Systems with multiple objectives.
Complexity Theory
The study of how critically interacting components self-organize to form potentially evolving structures exhibiting a hierarchy of emergent system properties.
Connectionist System
A system characterised by explicit connections between the components resulting in a distributed data structure (as used in neural networks).
The relation of an agent to its neighbours, it can be sparsely connected (only affected by a few neighbours), fully connected (interfacing with every other agent in the system) or some intermediate arrangement. This parameter critically affects the dynamics of the system.
A force of some sort restricting the movement of a system. See selection. In Life studies the variations of form do not allow infinite variation, something constrains the options available. Complexity studies seek the laws that apply, if any, in these cases and similar areas.
The idea that we construct our reality mentally rather than seeing directly an objective world. This idea is validated by research in neuropsychology and relates also to general semantics.
The idea that two agents can increase both their fitnesses by mutual help rather than by competition. This assumes that resources adequate for both exist, or are created by the interaction, and relates to synergy (synergic coevolution) and 'compositional evolution'.
Sexual mating between two genotypes in which a portion of the genes of one is joined to part of the genes of the other, to create a hybrid creature. This recombination allows rapid searching of the possible phase space.
The study of control or homeostasis within a system, typically using combinations of feedback loops. This can be within machines or living structures. First order cybernetics relates to closed systems, second order includes the observer perspective and third order looks to how these coevolve.
A system occupying a sequence of states in turn. A closed trajectory in state space.
Non-continuous. A step by step (countable) approach. Digital systems operate this way, with time steps being the controlling factor. A sufficiently large number of such steps can approximate to any continuous (analogue) system.
Using a resource flow to constantly achieve a task, which may be work (e.g. movement) or more usually to maintain the system in a steady state (e.g. a living organism). Dissipative systems operate far-from-equilibrium.
The range of features or niches available. This could be variation within a species, or the totality of different species in an ecosystem.
Downward Causation
Effect of higher level emergent properties on the lower level part behaviour. Constraints on the area of state space available.
The idea that issues can always be divided into either/or states, e.g. mind/matter, fact/value, right/wrong. A throwback to pre-complexity viewpoints and earlier bivalent logic and systemic valuation, replaced mostly in complex systems approaches by non-dualist (continuum) modes of thought that take into account the wider connectivity issues and the need to balance multiple objectives.
Dynamical Systems Theory
The mathematical study of the behaviour through time of systems. This studies the attractor structure, bifurcation behaviour and phase portraits of the system.
The behaviour of a system in time. Changes with time are the essence of complexity, a static system is merely a snapshot within an evolutionary continuum, however interesting it may be in its own right.
The relatively stable balance of different species within a particular area. A food chain, usually cyclic and self-sustaining.
Edge of Chaos (EOC)
The tendency of dynamic systems to self-organise to a state roughly midway between globally static (unchanging) and chaotic (random) states. This can also be regarded as the liquid phase, half way between solid (static) and gas (random) natural states. In information theory this is the state containing the maximum information.
System properties that are not evident from those of the parts. A higher level phenomena, that cannot be reduced to that of the simpler constituents and needs new concepts to be introduced. This property is neither simply an aggregate one, nor epiphenomenal, but often exhibits 'downward causation'. Modelling emergent dynamical hierarchies is central to future complexity research.
The tendency of systems to lose energy and order and to settle to more homogenous (similar) states. Often referred to as 'Heat Death' or the 2nd Law of Thermodynamics.
The surroundings of the system, including other systems and natural features. This context affects the direction of coevolution.
The effect of one variable on another, an interdependence between components rather than an independence.
The tendency of a system to settle down to a steady state that isn't easily disturbed, an attractor. Traditionally, equilibrium systems in physics have no energy input and maximise entropy, usually involving an ergodic attractor, but dissipative systems maintain steady states far-from-equilibrium (also non-equilibrium).
Visits every point in phase space with equal probability. The basis of entropy and the opposite to the behaviour of complex systems.
Evolutionary Stable Strategy, a system that resists disturbance, a stable balance between the various interacting agents in an ecosystem.
This is a universal idea, generalised as 'general selection theory' to be the process of 'variation, selection, retention' underlying all systemic improvement over time (including 'trial and error' learning). The term is often specifically applied however to genetic evolution where some changes, by being more efficient in functional ways, are preferred by natural selection.
Evolutionary Theory
The study of evolution based upon neo-Darwinian ideas. Modern complexity science adds additional self-organizational concepts to this theory to better explain organizational emergence.
Evolutionary Computation
A set of techniques, using ideas from natural selection, within computer science. Includes genetic algorithms, genetic programming, classifiers, evolutionary programming and evolutionary strategies.
Evolutionary Psychology
The study of how biological evolution and genetic development affects mind function and social behaviour.
Extrinsic Value
A form of judgement that allows a continuum of possibilities, i.e. a measurement of goodness or presence. This corresponds to fuzzy logic operations.
A term used to denote the tendency of systems to grow more organised, in opposition to the entropy expectation. Also called 'ectropy', 'enformy', 'negentropy' or 'syntropy' (or more generally 'self-organization'). The reasons for this are partly the motivation behind Complexity Theory.
A linking of the output of a system back to the input. Traditionally this can be negative, tending to return the system to a wanted state, or positive tending to diverge from that state. Life employs both methods.
Finite State Machine
A machine with a fixed number of internal options or possibilities. These could be as few as 2 (Yes/No) or any number of separate possibilities, each determined by some combination of input parameters.
The ability of an organism to survive and flourish in its current environmental conditions, relative to the other creatures also there. A measure of 'quality of life'.
Fitness Landscape
The number of separate niches available within an organism's phase space, often regarded as peaks on a landscape. The higher the peak, the better the option, the steeper the slope the greater the selection pressure.
The phenomenon of bird flocking can be explained by simple rules telling an agent to stay a fixed distance from a neighbour. The apparently intelligent behaviour of a flock navigating an obstacle follows directly from the mindless application of these rules.
The movement of resources from a place of high concentration to a low (e.g. energy goes from hot to cold). By utilising such flows systems can perform work (including self-organization). When flows in opposite directions balance, the system can arrive at the steady state (dynamic equilibrium) that characterises dissipative systems.
A System having similar detail at all scales, leading to intricate patterns and unexpected features. Fractal geometry explores systems with non-integer dimensions.
Fuzzy Logic
A way of dealing with uncertain information and variables that do not permit simple yes/no categorisations (e.g. colour). Can also be used to make decisions where uncertainty occurs (fuzzy control). This is a form of non-Aristotelian logic (see general semantics).
Game Theory
The study of interactions between intelligent agents, concentrating on whether outcomes are zero, positive or negative sum.
General Semantics
The study of how the way we use language constrains our thought patterns. It especially emphasises the need to adopt a non-Aristotelian viewpoint if we are to escape the errors of dualism. This relates to the new paradigm thinking behind complexity science and stresses that our 'maps' of reality are not equal to the 'territory' but are always only restricted viewpoints. See constructivism also.
General Systems Theory (GST)
The interdisciplinary idea that systems of any type and in any specialism can all be described by a common set of ideas related to the holistic interaction of the components. This nonlinear theory rejects the idea that system descriptions can be reduced to linear properties of disjoint parts.
Genetic Algorithm (GA)
The use of evolutionary techniques to diversify, combine and select options in order to improve performance, following the methods of natural selection by coding options as genes.
Genetic Programming
A form of variable length GA that uses directly acting program instructions as the genes.
The combination of genes that make up an organism. This has no form itself but directs the creation of the phenotype following the interaction of system, dynamics and environment. Usually regarded as comprising a number of alleles or bits (systems having two states, 0 or 1, off or on).
Global Optimum
The very best possible fitness over the entirety of state space.
A weblike branching structure where multiple owners are possible and loops may form. A N:M structure.
A treelike branching structure where each component has only one owner or higher level component. A 1:N structure.
Hill Climbing
The ability of mutation to increase the fitness of a agent, such that it climbs to a higher position on the fitness landscape.
Holarchic Value
A form of judgement that takes into account all the values present within all the entities that form the hypersystem, plus their interactions, a 'whole systems' valuation or fitness measurement of the multi-level whole.
Resistance to change. The ability of a system to self-regulate and maintain a particular state.
A set of systems interconnected and evolving together. The dynamic term we use for this is hypersystem.
Iterated Function System. A mathematical method of applying affine transformations to a seed to obtain a fractal image. Fractal compression works in reverse to derive an appropriate seed and transformation from the original image.
Intrinsic Value
A form of judgement that takes into account all the values present within the system, an holistic valuation or fitness measurement of the whole.
A loop that uses the current value of a system to derive its future value by re-inserting it into the equations controlling the system dynamics. Feedback. The linking of effect back to cause.
Julia Set
The inverse of the Mandelbrot set, using a single point from that set to generate a new unique set.
Lindenmayer systems allow simple rules to serve as a way of generating complex images by iteration. This can create extremely natural forms, flowers, trees etc.
A game invented by John Conway, it uses cellular automata to evolve lifelike patterns. It is also a universal computer and can in theory execute any program imaginable, given a large enough pattern.
Local Interaction
A property of agents that restricts them to reacting only to those other agents immediately adjacent. Most agents in alife systems behave this way.
Local Optimum
An easily found optimum in state space, but not guaranteed to be the global optimum.
Lotka-Volterra System
Equations that model population cycling in co-evolutionary systems. Forms cover predator-prey, war games and epidemics.
Mandelbrot Set
The mapping of the behaviour of a specific complex formula across space by colour coding the result of each starting point as convergent or divergent, generating a fractal boundary.
Transforming a input to an output by following a rule or look-up table. Also the selective study of 'reality'.
Storage of information or resource in such a way as to allow it to be reused at a later date.
A prefix used to denote a higher level of thought about the subject, e.g. metascience (where we consider how we approach science), meta-ethics where we consider how we define normative behaviour. Each level in a complex system can be considered as a meta-viewpoint upon the previous level of emergence. Relates to category or type theory and higher-order logic.
The need to take into account many conflicting variables in order to obtain an optimum fitness. This is a problem due to epistasis.
The random change of any part of the genotype, typically by reversing the state of one bit. Natural systems often mutate by the action of radiation, cosmic rays or carcinogenic agents.
The manufacture of systems of molecular size that emulate the behaviour of larger systems. Any alife system is potentially creatable in these dimensions, using standard biological or even inorganic components.
Natural Selection
The three stage process of variation, selection, reproduction (or persistance) that underlies evolution in all areas (in biology the synthesis of Medelian genetics with natural selection is called neo-Darwinism). It is combined within complex systems thinking with self-organization.
Negative Sum
The idea, from game theory, that agents combine in such a way that both lose or that the total change is a reduction in overall fitness, sometimes called dysergy or 'lose-lose'. Related to competition, where if the interactions repeat then we have escalating trajectories of fitness losses.
Connected systems, the properties of which do not entirely depend on the actual units involved but on the dynamics of the interconnections.
Neural Network
A simplified emulation of the connections of the human brain, used for investigating learning and self-organisation within an artificial environment.
Neutrosophic Logic
A new form of logic that goes beyond fuzzy logic by adding an axis for indeterminacy and thus takes into account not only what is measured but also what is not, a more whole systems or intrinsic logic better suited to complex systems.
A form of philosophy that emphasises paradox and the complementary and contextual nature of truth. This fits in with the idea of balance, emphasised within complex systems in the notion of 'edge-of-chaos'.
A peak in the ecological fitness landscape occupied by one variety of creature, often unopposed. Niches, in coevolutionary thought, are created by the organism interactions, do not exist in isolation and are a way of maximising group fitness by minimising competition (see synergy).
A system driven by energy flows away from a steady state of maximum entropy. Also called far-from-equilibrium.
Systems that behave in an unexpected way, not changing proportionally to a change in input. Sometimes going down when you expect them to go up, doing nothing instead, or changing drastically with only minor changes to the input. Nonlinear systems fail the mathematical principle of 'superposition'.
Having a non-homogeneous (uneven) distribution in space and/or time (exhibits patterns).
Having parts that are not the same in function or behaviour (varied rules or laws).
Non-Zero Sum
A situation in which it is possible for all participants to win or lose simultaneously, so that the fitness scores may total to a positive or negative sum overall.
Open Systems
Allowing resources (e.g. material or information) to enter or leave the system, sucking in resources from outside or giving out more than they take in.
A state that is the best fit for the current situation, the top of the local fitness landscape. All minor changes make the solution worst.
The search for the global optimum, or best overall compromise within a (typically) multivalued system. Where interactions occur many optima are typically present (the fitness landscape is 'rugged') and this situation has no analytical solution, generally requiring adaptive solutions.
The path taken by a cyclic attractor. A regular sequence that once entered cannot be exited without perturbation.
Organic System
A form of system that is autonomous and adaptive, based upon biological ideas rather than mechanical ones.
A non-random arrangement of parts, generally serving a purpose or function. The restriction of the system to a small area of its state space.
Several agents acting at the same time independently, simultaneous computation similar to that which happens within living systems.
A set of equivalent optimised solutions that all have the same global fitness but embody different compromises or niches between the objectives
A forced change to a system. This can result in a sudden shift to a new state, an immediate return to the old state or a long transient resulting in one or the other.
Phase Space
All the possibilities available to the system in theory. The sum total of possible states the system can occupy. In complex systems only a very small proportion of such states are found - the system is said to occupy only a minute proportion of state or phase space.
Phase Transition
A movement between static, ordered or chaotic states or back again. Usually used in connection with a change of state in physics from solid, to liquid, to gas or the reverse, but of general applicability in complexity theory.
The form of the organism. A result of the combined influences of the genotype and the environment on the self-organizing internal processes during development.
Positive Sum
The idea, from game theory, that when agents interact they can both benefit, the whole being greater than the sum of the parts, also called synergy or 'win-win'. When the interactions repeat we have escalating trajectories of positive fitness effects.
Prisoners Dilemma
A problem whereby a prisoner gets freedom by giving evidence against a fellow villain, but only if the fellow prisoner does not do the same. If both keep quiet a better overall result will obtain than either if both confess, or if just one confesses; yet for an individual the best result is still to confess. An example of a non-zero sum game, where cooperation pays both parties.
The chance of obtaining a particular result, e.g. if a 10 sided die is thrown it will be 10%. For complex problems there can be many outcomes, some of which do not seem to be ever realised, even if they appear to be equally probable.
A change taking place in time, such that an input is transformed to an output. This can be cyclic if the sequence of changes is such that the output recreates the input (such as autocatalysis).
Process Thought
The treatment of reality as the evolution of processes rather than the behaviour of objects. In this methodology we recognise that 'things' are simply standing waves (attractors) in a continuous dynamical process and have no inherent absolute properties.
The ability of a system to suffer degradation without altering its state. The ability to withstand perturbation without damage.
A choice between available options based on consideration of fitness within the current environmental context. A bias on movement in state space. See evolution.
Self-Organized Criticality (SOC)
The ability of a system to reach edge-of-chaos by self-organization.
Ability to create structure without any external pressures, an emergent property of the system. Related to extropy or negentropy. Internal constraints.
Self-Organizing Systems (SOS)
Systems that generate their form by a process of self-organisation, either wholly or in part.
Appearing the same at all magnifications. Fractal boundaries have this feature.
The unstable boundary between two attractors.
Modelling a system by implementing in a computer some relevant features. If all features are operational then the system is real not a simulation. Alife is sometimes said to be real life under this definition, unlike say a model of a volcano which cannot melt the computer - a feature of real volcanic lava, which is not included in the model.
Unchanging with time. This can be a static state (nothing changes) or a steady state (resource flows occur). In complex non-equilibrium systems we have multistable states, i.e. many semi-stable positions possible within a single system.
State Space
The total theoretical possibilities available to the system, by combinations of the parts. Also called phase space.
Strange Attractor
An attractor whose variables never exactly repeat their values but always are found within a restricted range, a small area of state space.
Random or unpredictable effects, often associated with probabilistic or statistical treatments.
A more open form of self-maintenance than autopoietic, more appropriate for social and ecological forms of organization. Exhibits more diffuse structures and fuzzy boundaries.
The use of geometric ideas within a systems view to describe and understand reality. Closely associated with Buckminster Fuller who applied it also to human behaviour.
The idea that combined parts have properties that are more or less that the sum of the parts (positive-sum or negative-sum rather than zero-sum). Related to emergence but much wider. The negative-sum version is sometimes called dysergy, leaving synergy to mean only beneficial effects also studied as symbiosis, 'holistic darwinism', 'synergistic selection', 'synergic evolution', 'cooperative coevolution' or 'compositional evolution' and many combinations thereof.
Made up of parts. Assembled. More than the sum of the components. Opposite of analytic (taking apart).
A collection of interacting parts that forms an integrated and consistent whole, isolatable from its surroundings. The concept of dynamics or change over time is central to our treatment of complex systems.
System Dynamics
The study of how systems actually behave, using models to simulate the assumptions and rules being followed. Often the behaviour seen is very different than the behaviour people expect.
Systemic Value
A form of judgement that allows only two possibilities, good or bad (present or absent, in or out). This corresponds to Boolean operations (based upon Aristotelian logic).
Systems Thinking
The systems approach relates to considering wholes rather than parts, taking all the interactions into account, see also General Systems Theory. It considers processes rather than things to be primary.
The path through state space taken by a system. It is the sequence of states or path plotted against time. Two general forms affect fitness, positive-sum and negative-sum.
A short term phenomena seen on the way towards, and before reaching, a steady state.
Transient Attractor
An temporary attractor formed within the transient behaviour of a system. This is a state (like a glider in the Game of Life) that only persists for a short time before dissipating with new perturbations (e.g. a smoke ring). Most attractors in evolving complex systems are of this type, due to the presence of continual perturbations.
Turing Machine
A form of universal computer, assumed to take its instructions from an infinite paper punched tape and output results to the same medium before stopping upon completion of the program.
Universal Computer
A computer able to perform any task if suitable programmed. Most personal computers are of this type (at least for a small range of tasks). Any system with sufficient flexibility of interaction may perform this function, for example some automata or neural networks.
Universal Constructor
A machine able to construct any other object (including a copy of itself) give the appropriate instructions.
The dimensions or objectives we choose with which to measure the system and those variables we attempt to optimise in deriving fitness. Due to neural associations, the often imagined dualism between 'fact' and 'value' is invalid, thus values (purposes) can and should form a part of our scientific worldview.
Whole Systems
The inclusion in our definition of 'system' of all the issues involved, including all the nested levels of interconnected smaller systems and how they relate to each other and work dynamically as a whole.
Zero Sum
The idea, from game theory and economics, that agents swap resources, so that what one loses the other gains leaving a net no-change in fitness (contrast with non-zero, positive and negative sums).

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