A system in which the later states of the system follow from or are determined by the earlier ones. Such a system is described in contrast to the stochastic or random system in which future states are not determined from previous ones. An example of a stochastic system would be the sequence of heads or tails of an unbiased coin or radioactive decay. If a system is deterministic, this doesn’t necessarily entail that later states of the system are predictable from knowledge of the earlier ones. In this way, chaos is similar to a random system. For example, chaos has been termed “deterministic chaos” since, although it is determined by simple rules, its property of sensitive dependence on initial conditions makes a chaotic system largely unpredictable.

See: Chaos; Randomness

Bibliography: Goldstein in Sulis and Combs (1996); Lorenz (1993)

A group process technique developed by the organizational/complexity theorist Jeffrey Goldstein that facilitates self-organization by generating far-from-equilibrium conditions in a work group. The process consists of several methods whereby information is amplified by highlighting the differences in perception, idea, opinion, and attitude among group members. Difference questioning does not aim at increasing or generating conflict, but, instead, tries to uncover the already differing standpoints. Moreover, the process takes place within boundaries that ensure the self-organization is channeled in constructive directions. Difference Questioning aims at interrupting the tendency toward social conformity which robs groups of their creative idea generating and decision-making potential. In other words, it strives to allow a greater flow of information among the group members which has been shown to be correlated with a far-from-equilibrium condition, i.e., a condition in which self-organizing change can take place.

See: Information; Self-organization

Bibliography: Goldstein (1994)

The term used by the Prigogine School (from Ilya Prigogine, winner of the Nobel Prize in chemistry) for emergent structures arising in self-organizing systems. Such structures are dissipative by serving to dissipate energy in the system. They happen at a critical threshold of far-from-equilibrium conditions. An example is the hexagonal convection cells that emerge in the Benard System when it is heated. Another example are the so-called “chemical clocks” demonstrated in the Belousov-Zhabotinsky reaction. These “chemical clocks” are composed of both temporal structures such as a shift from one color to another with the regular of a clock as well as spatial structures such as spiral waves and so on.

See: Coherence; Emergence; Far-from-equilibrium

Bibliography: Prigogine and Stengers (1984); Nicolis in Davies (1989)

A complex, interactive system evolving over time through multiple modes of behavior, i.e., attractors. Instead, therefore, of conceiving of entities or events as static occurrences, the perspective of a dynamical system is a changing, evolving process following certain rules and exhibiting an increase of complexity. This evolution can show transformations of behavior as new attractors emerge. The changes in system organization and behavior are called bifurcations. Dynamical systems are deterministic systems, although they can be influenced by random events. Times series data of dynamical systems can be graphed as phase portraits in phase space in order to indicate the “qualitative” or topological properties of the system and its attractor(s). For example, various physiological systems can be conceptualized as dynamical systems, the heart for one. Seeing physiological systems as dynamical systems opens up the possibilities of studying various attractor regimes. Moreover, certain diseases can be understood now as “dynamical diseases” meaning that their temporal phasing can be a key to understanding pathological conditions.

See: Attractors; Bifurcation; Logistic Equation

Bibliography: Abraham, et. al. (1991); Guastello (1995); Peak and Frame (1994)

A term made popular by researchers at the Santa Fe Institute to indicate a particularly “pregnant” phase in the evolution of a dynamical, complex system where creative emergence of new structures is at a maximum. In the study of the behavior of cellular automata and similar electronic arrays, the edge of chaos seems particularly favorable for the emergence of innovative, more adaptive structures and modes of functioning. The edge of chaos is conceived as that zone between too much rigidity and too much laxity. There is controversy whether natural systems have a tendency to evolve into edge of chaos conditions. The edge of chaos can also be considered as roughly analogous to far-from- equilibrium conditions in that they both represent critical thresholds where self-organization and emergence are heightened. Organizational applications have to do with processes that encourage organizational innovation by facilitating edge of chaos like conditions.

See: Cellular Automata; Far-from-equilibrium

Bibliography: Kauffman (1995); Lewin (1992); Waldrop (1992)

The arising of new, unexpected structures, patterns, or processes in a self-organizing system. These emergents can be understood as existing on a higher level than the lower level components from which the emergents emerged. Emergents seem to have a life of their own with their own rules, laws, and possibilities unlike the lower level components. The term was first used by the nineteenth century philosopher G.H.Lewes and came into greater currency in the scientific and philosophical movement known as Emergent Evolutionism in the 1920’s and 1930’s. In an important respect the work connected with the Santa Fe Institute and similar facilities represents a more powerful way of investigating emergent phenomena. In organizations, emergent phenomena are happening ubiquitously yet their significance can be downplayed by control mechanisms grounded in the officially sanctioned corporate hierarchy. One of the keys for leaders from complex systems theory is how to facilitate emergent structures and take advantage of the ones that occur spontaneously.

See: Self-organization

Bibliography: Cohen and Stewart (1994); Goldstein in Sulis and Combs (1996)

Equilibrium is a term indicating a rest state of a system, for example, when a dynamical system is under the sway of a fixed or periodic attractor. The concept originated in Ancient Greece when the great mathematician Archimedes experimented with levers in balance, literally “equilibrium”. The idea was elaborated upon through the Middle Ages, the Renaissance and the Birth of Modern Mathematics and Physics in the 17th and 18th centuries. “Equilibrium” has come to mean pretty much the same thing as stability, i.e., a system that is largely unaffected by internal or external changes since it easily returns to its original condition after being perturbed, e.g., a balanced lever on a fulcrum (i.e., a see-saw). More generally, equilibrium suggests a system that tends to remain at status quo.

See: Attractor; Far-from-equilibrium

Bibliography: Goldstein (1994); Prigogine and Stengers (1984).

The term used by the Prigogine School for those conditions leading to self- organization and the emergence of dissipative structures. Far-from-equilibrium conditions move the system away from its equilibrium state, activating the nonlinearity inherent in the system. Far-from-equilibrium conditions are another way of talking about the changes in the values of parameters leading-up to a bifurcation and the emergence of new attractor(s) in a dynamical system. Furthermore, to some extent, far-from-equilibrium conditions are similar to “edge of chaos” in cellular automata and random boolean networks.

See: Difference Questioning; Equilibrium; Purpose Contrasting; Self-organization

Bibliography: Goldstein (1994); Nicolis in Davies (1989); Prigogine and Stengers (1984)

The mutually reciprocal effect of one system or subsystem on another. Negative feedback is when two subsystems act to dampen the output of the other. For example, the relation of predators and prey can be described by a negative feedback loop since the more predators there are leads to a decline in the population of prey, but when prey decrease too much so does the population of predators since they don’t have enough food. Positive feedback means that two subsystems are amplifying each other’s outputs, e.g., the screech heard in a public address system when the mike is too close to the speaker. The microphone amplifies the sound from speaker which in turn amplifies the signal from the microphone and around and around. Feedback is a way of talking about the nonlinear interaction among the elements or components in a system and can be modeled by nonlinear differential or difference equations as well as by the activity of cells in a cellular automata array. The idea of feedback forms the basis of System Dynamics, a way of diagramming the flow of work in an organization founded by Jay Forrester and made popular by Peter Senge.

See: Interactive, Nonlinear

Bibliography: Eoyang (1997)

A “graphical” way to measure and explore the adaptive (fitness) value of different configurations of some elements in a system. Each configuration and its neighbor configurations (i.e., slight modifications of it) are graphed as lower or higher peaks on a landscape-like surface, i.e., high fitness is portrayed as mountainous-like peaks, and low fitness is depicted as lower peaks or valleys Such a display provides an indication of the degree to which various combinations add or detract from the system s survivability or sustainability. The use of fitness landscapes in understanding the behavior of complex, adaptive systems has been pioneered by Stuart Kauffman in his study of random boolean networks. An important implication from studying fitness landscapes is that there may be many local peaks or “okay” solutions instead of one, perfect, optimal solution. Thinking in terms of fitness landscapes can point to foolish adaptation, i.e., a downward trend on the slopes of the peaks. Moreover, studies of N/K models using fitness landscapes demonstrates that there is a decreasing rate of finding fitter adaptable configurations as one travels uphill on a fitness landscape. The use of fitness landscapes can be applied to gain insight into various organizational issues including which innovative organizational designs, processes, or strategies promise greater potential.

See: N/K Model; Random Boolean Networks

Bibliography: Kauffman (1995); Kauffman and Macready (1995); Maguire (1997).

A geometrical pattern, structure, or set of points which is self-similar (exhibiting an identical or similar pattern) on different scales. For example, Benoit Mandelbrot, the discoverer of fractal geometry, describes the coast of England as a fractal, because as it is observed from closer and closer points of view (i.e., changing the scale), it keeps showing a self-similar kind of irregularity. Another example is the structure of a tree with its self- similarity of branching patterns on different scales of observation, or the structure of the lungs in which self-similar branching provides a greater area for oxygen to be absorbed into the blood. Strange attractors in chaos theory have a fractal structure. The imagery of fractals has been popularized by the fascinating graphical representations of fractals in the form of Mandelbrot and Julia Sets on a personal computer.Unlike the whole number characteristic of our usual dimensions, e.g., two or three dimensional drawings, the dimension of a fractal is not a whole number but a fractional part of a whole number such as a dimensionality of 2.4678.