The Spectrum of Complex Behaviour

Complex behaviour is by its nature continually changing; however we can envisage a spectrum of complex behaviour that has several fuzzy regions that typify the system’s behaviour at a point in time and also describe an increase or decrease in certain behavioural characteristics.

spectrum of complexity image 2
Ordered

The ordered domain is highly predictable at all times and is robust to reasonable change or perturbation and its response to such perturbations is also reasonably predictable. The ordered domain may also show highly regular or cyclic behaviour. This behaviour is usually considered to define a simple and stable system.

Low Complexity

The low complexity domain starts to exhibit more intricate cyclic behaviour (cycles within cycles) which become more difficult to predict at some scales and at some times, but in general it is still pretty predictable. The sensitivity to change has increased and it requires a smaller perturbation to illicit an unexpected response when compared to an ordered system. The general range of behaviours is still limited.

Medium Complexity

Medium complexity means that the periods of time over which the system is predictable are decreasing as is the period of time that such predictions are reasonably accurate. We also start to see occasional and unique behaviours of greater magnitude. The system is more sensitive to increasing small perturbations and its response to such changes is also increasingly unpredictable.

High Complexity

As we enter a high complexity region the number of extreme events increase and the ability to predict the behaviour of the system is continuing to decrease to a point where only long term statistical predictions of very short term predictions have any meaning.  At this point the system is extremely sensitive to small perturbations and its response to such change is unpredictable. Eventually we may reach a point  termed, ‘the edge of chaos’, but this is a much overused concept that in fact has little scientific meaning other than for computational systems (see my blog). However if the system is capable of chaotic behaviour it is possible that there is stage of high complexity where the system oscillates between various periods of time in highly complex and chaotic states. There are views that it is in this domain that amazing things can happen and systems of complex components can self-organise into complex and stable structures and behaviours. It is most certainly true that self-organisation does occur, however to my knowledge there is little scientific evidence that suggests that this happens for all types of system, or that it occurs in this region.

Deterministic Chaos

Eventually the system may become unpredictable other than statistically over very large periods of time. This is sometimes considered to be ‘random’ behaviour, however if you analyse the behaviour there are subtle patterns that are very difficult to detect. This domain is called deterministic chaos because we are still talking about systems for which we know a lot even though its behaviour is pseudo- random. Eventually, and given sometimes thousands or even millions of years this chaotic behaviour will have repeating patterns, whereas true randomness never repeats

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