Self-Organization, Complexity, and Emergent Systems

Judging from the logistic equation, most orderly features of chaos depend strictly on the control parameter. For a given value of that parameter, the order develops spontaneously, that is, without external cause. Such spontaneous development seems to be a special class of an interesting process called self-organization. Selforganization is the act whereby a self-propagating system, without outside influence, takes itself from seeming irregularity into some sort of order. It seems to reflect a tendency for a dynamical system to organize itself into more complex structures. The structure can be spatial, temporal, or operational (functional). The time over which the structure lasts varies from one case to another.
Examples of self-organization are the organizing of birds into an orderly flock, of fish into a clearly arranged school, of sand particles into ripple marks, of weather elements (wind, moisture, etc.) into hurricanes, of water molecules into laminar flow, of stars into the spiral arms of a galaxy, and of the demand for goods, services, labor, salaries, and so on, into economic markets. Briggs & Peat (1989) cite, as other examples:
• the lattice of hexagonal cells that form after the onset of chaos by heating a pan of liquid from below
• successions of ordered or oscillatory regimes that follow chaos in various chemical reactions
• termite nests resulting from random-like termite activity
• rush-hour traffic patterns following less-busy, earlier random-like traffic
• organized amoeba (slime mold) migrations appearing after random-like aggregation.
Self-organization is a main feature of a kind of behavior called complexity. In this specialized sense, complexity (Lewin 1992, Waldrop 1992) is a type of dynamic behavior that never reaches equilibrium and in which many independent particle-like units or ''agents" perpetually interact and seek mutual accommodation in any of many possible ways. The units or agents spontaneously organize and reorganize themselves in the process into ever larger and more involved structures over time. "Complex" dynamic behavior has at least six ingredients:

• A large number of somewhat similar but independent items, particles, members, components or agents.
• Dynamism—the particles' persistent movement and readjustment. Each agent continually acts on and responds to its fellow agents in perpetually novel ways.
• Adaptiveness: the system conforms or adjusts to new situations so as to insure survival or to bring about some advantageous realignment.
• Self-organization, whereby some order inevitably and spontaneously forms.
• Local rules that govern each cell or agent.
• Hierarchical progression in the evolution of rules and structures. As evolution goes on, the rules become more efficient and sophisticated, and the structure becomes more complex and larger. For instance, atoms form molecules, molecules form cells, cells form people, and thence to families, cities, nations, and so forth.
Because of those characteristics, complex adaptive systems are called emergent systems. Their chief characteristic is the emergence of new, more complex levels of order over time. Complexity, like chaos, implies that we can't necessarily understand a system by isolating its components and analyzing each component individually. Instead, looking at the system as a whole might provide greater—or at least equally helpful—insight.
Authors used to categorize dynamical behavior either as orderly (e.g. having a fixed-point or periodic attractor) or random (Crutchfield & Young 1989). Chaos and complexity are important additional types. So, as of today, dynamical behavior might be classified into order, complexity, chaos, and randomness. In fact, those four types might form a progression or hierarchy, in the order just listed. Also, the four types aren't mutually exclusive. Orderly, chaotic, and random-like behavior, for instance, all have elements of determinism. Similarly, complexity and chaos both contain order and randomness.
To the extent that there is order within the chaotic regime, the word chaos (since its normal usage implies utter confusion or total disorder) is a misnomer. But it's too late now.