The main current scientific theory related to self-organization is Complexity Theory, which states:
Critically interacting components self-organize to form potentially evolving structures exhibiting a hierarchy of emergent system properties.
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3. Edge of Chaos
A point at which system properties change suddenly, e.g. where a matrix goes from non-percolating (disconnected) to percolating (connected) or vice versa. This is often regarded as a phase change, thus in critically interacting systems we expect step changes in properties.
The ability of a system to evolve in such a way as to approach a critical point and then maintain itself at that point. If we assume that a system can mutate, then that mutation may take it either towards a more static configuration or towards a more changeable one (a smaller or larger volume of state space, a new attractor). If a particular dynamic structure is optimum for the system, and the current configuration is too static, then the more changeable configuration will be more successful. If the system is currently too changeable then the more static mutation will be selected. Thus the system can adapt in both directions to converge on the optimum dynamic characteristics.
This is the name given to the critical point of the system, where a small change can either push the system into chaotic behaviour or lock the system into a fixed behaviour. It is regarded as a phase change. It is at this point where all the really interesting behaviour occurs in a 'complex' system, and it is where systems tend to gravitate give the chance to do so. Hence most ALife systems are assumed to operate within this regime.