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Complex Systems

The field of "complex systems" is not so defined precisely. It often includes " Chaos ", "Fractal" and "Cell Automaton". But those studies are very small parts of the complex systems in the world.

The name of this study field, "Complex systems", makes us to think that this field solve all complex phenomena in the world.

But this field is not so powerful. Main themes of this field is that "Complex movement made by easy functions" and "Complex movement made by easy laws".


Fractal is a picture with self similarity. Fractal is interesting as an art, but it is used as a technique of image processing. Mathematically, fractal is something a part of chaos.

Self Organization

"Organization" is opposite concept of chaos. The nature has self organization skill. Patterns are made by self organization.

If entropy increase law is only the rule of the natue, organization dose not appear. But self organization appears. The nature is mysterious.

Pattern Recognition and Self Organized Mapping (SOM) are the methods related to self organization.

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