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FRACTALS: USEFUL BEAUTY

(FRACTAL GEOMETRY)

Fractals is a new branch of mathematics and art. Perhaps this is the reason why most people recognise fractals only as pretty pictures useful as backgrounds on the computer screen or original postcard patterns. But what are they really?

Most physical systems of nature and many human artifacts are not regular geometric shapes of the standard geometry derived from Euclid. Fractal geometry offers almost unlimited ways of describing, measuring and predicting these natural phenomena. But is it possible to define the whole world using mathematical equations?

This article describes how the four most famous fractals were created and explains the most important fractal properties, which make fractals useful for different domain of science.

Many people are fascinated by the beautiful images termed fractals. Extending beyond the typical perception of mathematics as a body of complicated, boring formulas, fractal geometry mixes art with mathematics to demonstrate that equations are more than just a collection of numbers. What makes fractals even more interesting is that they are the best existing mathematical descriptions of many natural forms such as coastlines, mountains or parts of living organisms.

Although fractal geometry is closely connected with computer techniques, some people had worked on fractals long before the invention of computers. Those people were British cartographers, who encountered the problem in measuring the length of Britain coast. The coastline measured on a large scale map was approximately half the length of coastline measured on a detailed map. The closer they looked, the more detailed and longer the coastline became. They did not realise that they had discovered one of the main properties of fractals.

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