Mandelbrot fernfernComplexity Pages
A non-technical introduction to the new
science of Chaos and Complexity

Victor MacGill
Victor MacGill
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Go to tutorial A basic tutorial about chaos and Complexity which covers the main topics.
 

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The Mandelbrot Set

Complex Adaptive Systems



Wolfram’s class four cellular automata are examples of complex systems known as complex adaptive systems. A Complex Adaptive system is also a dissipative system, so it has all the qualities of a dissipative system, but a complex adaptive system is more complex and has more qualities other dissipative systems do not have.

A complex adaptive system not only has the ability to maintain its boundaries and sustain its own existence, but can also adapt and change itself to make it even more fit for it’s environment. In short, it is a system that can learn. A complex adaptive system will have some form of memory, whereby it can ‘remember’ what has happened in its history and use that information as a part of its strategy for acting more effectively in the present. Whether it is a bacterium sensing changes in the concentration of a particular chemical indication food in that direction or a university professor gaining an understanding of quantum physics, the process is still using information gained previously to be more effective in the present.

All life is made up of complex adaptive systems. Complex Adaptive systems are usually comprised of a large number of separate autonomous agents operating in their own interests, but also co-operating together as a whole functional unit. There is no “control centre” in charge of what happens. There is nobody or no-thing in charge to make decisions, and yet all the decentralised decisions necessary and all the co-operation necessary between the agents occurs. The intense and complex interactions between the agents that make up the organism, enable a process called “emergence” where the organism to act as one unit in a way not possible by the individual agents. It is only when the all work together dynamically that the overall system maximises its location on the phase space. Complexity takes what is complex and allows it to operate in simple ways.

The individual agents do not need to be intelligent for the system overall to be intelligent. The extra co-ordinated ability comes from the relationships between the agents. A complex adaptive system is run from the bottom up rather than top down. It is the individual agent that determine the overall shape of the system, even though the systems imposes restrictions on the individual agents in order that they the system functions as a whole unit.

Complex adaptive systems often develop into nested layers. All the agents interact together intensely such that new emergent, organism-wide attributes develop. Millions of ants work together such that the colony is capable of operating in ways no mere collection of ants could. The whole society works together so it can be seen as a single organism maximising its position in its environment. The newly created attributes themselves interact intensely so as to enable the emergence of yet another level of complexity growing out of the previous level. As this process continues each new layer emerges, nested in the previous layer. The whole system works as a single unit while the individual agents still operate autonomously and different parts work in together to form a whole multi-layered being.  The layers in a complex adaptive system typically form in a fractal fashion, so what happens at one level is mirrored at other levels.

The human body is an excellent example of a nested complex adaptive system. The agents that make up a complex adaptive system are often complex adaptive systems in their own right. The cell is the basic unit of life and it is a complex adaptive system with its own semi-permeable boundary that can allow necessary chemicals into the cell and prevent harmful ones from entering. It is sustained by this flow of energy. It is made up of self-sustaining elements such as the mitochondria, apparatus golgi and cell nucleus.

The cells them from together to create body tissue that works together in a new organism-wide system capable of operating in ways a collection of cells never could.

Different pieces of body tissue then congregate to form body organs that again are capable of co-ordinating the actions of the various body tissues in new emergent ways.

The body organs constellate to form body systems and those body systems them work together in extremely complex ways to form a new whole level of complex organisation; a human being.

A complex adaptive system is resilient in the face of perturbations from the environment that would cause less adaptive systems to disintegrate. It therefore does not need perfect conditions in which to live. It can change its own state to compensate for changes in the environment to increase its ability to survive. Furthermore, it has a memory and can learn from previous experience. A complex adaptive system can learn so it makes best advantage of its situation and can avoid many pitfalls that may exist in its environment.

Since a complex adaptive system starts in a complex state with many agents interacting which reduces to simple outputs, they are irreversible. We can not back engineer the system to see what it was like when it started, which may be possible for a chaotic system since it grows from the simple to the complex.

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