Variables in the mathematical equations used to model system behavior. Changes in the values of these variables can affect the system’s behavior.

An abstract mathematical space which is used to display time series data of the measurements of a system. The dimensions of phase or state space correspond to the number of variables used to characterized the state of the system. For example, the phase space of a pendulum would consist of two dimensions: the speed of the bob; and the distance of the bob from the vertical resting state. Phase space is very helpful for observing the patterns that result as systems evolve over time, including attractors. Please note that time is usually not one of the explicit dimensions of the phase space, a role, however, that time does play in a straight graphical depiction of a time series.

The geometrical patterns shown in phase space as a system evolves. These portraits may be attractors such as fixed point, periodic, and strange attractors. They can also include repellors (the opposite of attractors) and such interesting patterns as saddles (combination of attractor in one direction and repellor in another direction) and separatrices, or boundaries between two basins of attraction.

A type of mathematical pattern in which the frequency of an occurrence of a given size is inversely proportionate to some power (or exponent) of its size. For example, in the case of avalanches or earth quakes, large ones are fairly rare, smaller ones are much more frequent, and in between are cascades of different sizes and frequencies. Power laws define the distribution of catastrophic events in Self-organized Critical systems. According to Stuart Kauffman, systems at the "edge of chaos" will show a power law distribution, therefore, having this type of distribution can be evidence that systems are at this particularly "pregnant" phase.

A method developed by the management/complexity theorist Jeffrey Goldstein which consists of a work group highlighting the discrepancy between their original purpose and the current activities or procedures being done. The purpose of purpose contrasting is similar to difference questioning: to increase the amount of information in a system and thereby facilitate self-organization. For example, in a bureaucratically organized business or institution, the bureaucracy itself becomes its own purpose, obscuring the original purpose of making a product or providing a service.

Electronic arrays developed by the medical researcher and evolutionary biologist Stuart Kauffman. These arrays are used to study self-organizing processes and the emergence of new structures. It is from his study of these Boolean Networks plus borrowing from Wright s idea of fitness landscapes and work in solid state physics on spin glasses, that Kauffman derived his N/K model of complex systems. The Networks are random to the extent that input rules are set and changed at random in order to not bias the system in the direction of specifically planned structures.

The existence of repetitive patterns or structures. In an important sense, redundancy refers to order in a complex system in the sense that order is defined as the existence of structures that maintain themselves over time, i.e., they are stable. In Information Theory, redundancy refers to repetition in patterns of messages in a communication channel. If the message contains these redundancies, they can be compressed further, e.g., if a message contains a series of two hundred and fifty 1’s, then the message could be compressed into a command which effectively says "and then repeat 1 250 times, instead of writing out all two hundred fifty 1’s. Self-organizing processes demand some element of redundancy which can be considered as a "fuel" for the anacoluthian processes leading to emergence. In other words, novel patterns come from a recombination of redundant patterns.