## Chaos Theory as part of the nonlinear dynamics

Since the 80’s we know the chaos theory and fractals. Mandelbrot-set, the butterfly-effect and the fascinating images of fractals. At the end of the 80’s, during my studies I got the task to program with Pascal und Basic three-dimensional fractals. My interest was awoken. But where we do find today the so called chaos theory or chaos research?

It is about small changes in the starting conditions which lead to completely different results. In numeric Simulations e.g. in the fluid dynamics I could see such effects.
And then there it is again, the question if a flap oft he butterfly’s wing at the one end oft he world may cause a tornado at the other end? The butterfly-effect, which from small causes gives rise gigantic effects. And the chaos theory. The nature as dynamic organism instead as clockwork.

Following deterministic principles we can predict and calculate the behaviour of a system for a unlimited period of time, if we know it at a certain initial condition. But if the system with the smallest changes in the initial conditions behaves chaotic, then the time dependent development may be completely different and may not be predicted anymore.
The science an the practical application uses order in the chaotic behaviour, which may described by formulas and principles. For instance for the prediction of the finance markets, of traffic jams, of erosion, for the prediction of the spread of epidemics or for the improvement of the surgery in case of liver tumours. There it is interesting to read from Heinz-Otto Peitgen.

Therefore the chaos theory isn’t only aesthetic, but as part of the nonlinear dynamics useful, for the understanding and the development of predictions and may applied also for the health and live.
The landscapes in the video achievable with the button in the menu and the fractal images of the Website are calculated with Mandelbulb3D and should remind us that there isn‘t visible only aesthetic objects, but in the same time also fascinating developments which are possible because of such computational simulation calculations.

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