What is Geometrie of Fractals ?

1999-09-24

Geometry of Fractals is a young field of computer science. The concerns of Geometry of Fractals are hierarchical structures and similarities inside this structures (self-similarity).

The term 'Fractal' was introduced 1975 by the mathematician Benoid B. Mandelbrot. The term 'fractal' means broken (fragmented). It describes the characteristic of Fractals, to become more and more complex in the detail.

A Fractal Everyone who is using a computer has seen a Fractal like this before. They are calculated iteratively (in minimizing intervals of the complex parameter c) with the simple formula z -> z² + c.

Fractal mountains Pictures of mountains are generated with continously repetition of crinkling an area. Today, this kind of fractals is standard in producing movies.

Fractal Plants The picture shows a water-lily calculated on the principals of self-similarity. The fascinating correlations of the growth of plants and mathematics are described in the gorgeous book 'The Algorithmic Beauty of Plants'.

Geometry of Fractals and self-similarity are not only practical for producing beautyful pictures. The underlying principals can also be found in nature and can be applied in some very useful ways:
In a very similar manner for example, it is possible to calculate timely progressions ahead. The vhf-project of the Weather Forecast is an application based on correlations of Geometry of Fractals.