2. The Basic Paradigm of Self-organization

Recently, self-organization has been drawing attention in many research areas ranging from natural sciences to humanities. Several scientific research areas are concerned with self-organizing systems, such as dissipative structure theory [Pri 77], synergetics [Hak 78, Hak 83], the theory of molecule evolution [Eig 79], autopoiesis theory [Mat 80], bio-holonics [Shi 88] and natural and artificial neural networks. Jantsch [Jan 80] discusses a wide area of research on self-organization from a unified philosophical view, and indicates its direction for the future. These theories give us many suggestions for self-organization of computational systems. However, the main objects of these theories are natural systems, and there is large unsought research area between these systems and current computational systems.

Laszlo [Las 72] itemize four properties of natural systems. We believe artificial self-organizing systems should also have these properties. Thus, they are explained below from our point of view.

Although holisticity and self-stability are not mentioned explicitly in the rest of this paper, they are important as backgrounds of this work.

A generic macroscopic model of self-organizing systems [Kan 92a], which CCM is based on, is explained here. The model is shown in Figure 1. This model can be applied to a wide range of self-organizing systems, but not all of them. It models our target self-organizing computational system, a thermodynamic system that generates a dissipative structure, and other varieties of self-organizing systems.

Figure 1. Generic model of self-organizing systems

Self-organizing systems generate order in a macroscopic level. The degree of order should be measurable because if it is not, we cannot claim objectively that the system is self-organizing. Thus, entropy or (global) order degree, which is a measure of the order or degree of organization, should be defined. If entropy is defined, it decreases with time. If order degree is defined, it increases with time. If the system is a thermodynamic system, entropy must be ``thrown away'' from the system, because it must satisfy the second law of thermodynamics which states that entropy increases in a closed system. Thus, it must be an open system in this case.[*2.2]

There must be a set of laws or rules that (partially) control how the system changes, though they probably do not control the system in a deterministic way for reasons described later. Probably, the rules work at a microscopic level and their emergent behavior generates complex macroscopic behavior of the system. Thus, the system is hierarchical (or heterarchical). For simplicity in this paper, rules, such as natural laws, are asserted as given and unchanging.[*2.3] There will be various ways of describing the laws or rules. The laws can be written as differential equations in some systems, and may be written as sequences of operations in some others, and so on.

The growth of a self-organizing system is autonomous, and, thus, its behavior is unpredictable, or it is observed as nondeterministic or driven by noise that comes from the outside of the system. However, these properties are not sufficient conditions for self-organization, of course. If the behavior is predictable, i.e., observed as deterministic, it is not a self-organizing system, but the organization is fully controlled by external laws or rules. In particular, in the case of computational systems, deterministic systems are (indirectly) organized by humans, because the rules, i.e., the programs, are written by humans. This does not constitute self-organizing computation. In thermodynamic or other physical systems, nondeterministic system development is called bifurcation or symmetry breaking [Pri 77, Pri 84].

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(C) Copyright 1994 by Yasusi Kanada and IEEE
Y. Kanada