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Scientists try to penetrate natural phenomena with their understanding, seeking to reduce all complexity to a few fundamental laws. The cool rationality of science and technology has pervaded and transformed the world to such an extent that it could destroy human life.
The creed of the ¡§fundamentalists¡¨ has lost its exclusive attractiveness because of the great unifying success in modern science (e.g.: elementary particle physics, molecular genetics, ...). It becomes more and more important to figure out the patterns through which the basic laws show themselves in reality. More than just fundamental laws are operating in what actually ¡§is¡¨. Every non-linear process leads to forks in the path at witch decisions are made whose consequences can¡¦t be predicted because each decision has the character of an amplification. These decisions may blow up and have fear - reaching effects. Sooner or later the initial knowledge of the system becomes irrelevant, from now on there is an uncontrollable process, where information is generated and retained. These processes become unpredictable over very long periods of time. E. g.: The old problem of the stability of the solar system is still unsolved. (Problem of gravitational interactions) Analogous problems arise in almost all other disciplines. We have no controlled nuclear fusion because we have no adequate understanding of the chaotic motion of charged particle in the magnetic mirror system. Phenomenology has its own laws. At every new stage of organisation new rules take effect. We know it well from everyday live, but it calls for a completely new orientation in science.
On the one hand some people look upon a computer as a diabolical instrument and on the other hand are there some others that are completely addicted. But used with some reflection it can also help us lift the veil on nature¡¦s secrets.
Where scientists of earlier generations had to simplify their equations or give up completely, we are able to see their full content on the display monitor of our computer. Through graphical representation of natural processes new ideas and associations are stimulated. In connection with the computer a lot of new topics sprung up, like Synergetics. Synergetics is the systematically trying to find the rules by which order arises in complex systems.
Fractals are part of Synergetics. They deal with chaos and order and with their competition or coexistence. The process chosen here comes from various physical or mathematical problems, like order and disorder or magnetic and non - magnetic state. The pictures represent processes that are simplified idealisations of reality.
The principle of self - similarity is nonetheless realised approximately in nature: coastlines, riverbeds, cloud formations, trees, and so on. It was Benoit B. Mandelbrot who opened our eyes to the fractal geometry of nature.
The processes that generate fractals are simple feedback processes in which the same operation is carried out repeatedly.
For better imagination see the picture.
The only requirement here is a non - linear relation between input and output. The rule x "³f(x) will depend on a parameter c, whose influence won¡¦t be discussed here, because it would be to complex.
Our interest is now the behaviour of this iteration over a long period of time. What will the sequence do? Reach a limit value and rest there or be a typical cycle of values that is repeated over and over again? Or is it for all times unpredictable?
Physicists like to think in terms of infinitesimal time - steps: natura non facit saltus. Biologists often prefer to look at changes from year to year or from generation to generation. Both views are possible and only the circumstances stipulate which description is appropriate.
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