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Fractals

Fractals are mathematical structures which on an ever smaller scale infinitely repeat themselves. To explain how a fractal is formed the so-called Von Koch-curve is very suitable. The start is a line segment:

Von Koch01
divide it in 4 new line segments according to a fixed pattern:
Von Koch02

repeat this as often as you like:

Von Koch03

Von Koch04

Von Koch05

 

 

Relatively simple formulas may create the most spectacular figures. For example:


 

Apart from artistic applications fractals are very useful in the area of mathematics that is called chaos theory (see also backgrounds). The characterisation of apparently disorderly structures (e.g. small parts with a very rough surface, coastlines, the structure of branches and  leaves) makes grateful use of fractal mathematics as well.

 

fractal branches01 fractal branches02

 

 

 

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