INTRODUCTION TO FRACTAL GEOMETRY


Fractals in nature

However, fractals are not something that come out from the computer or the minds of people programming them. computers have just enabled us to portray these geometries that are actually quite natural. As a matter of fact it was really only after discovering the fractals with computers that an interest towards fractal geometry in nature was grown in a larger scale. Trees, sea shells, coast lines and branching rivers are just a few examples of natural fractals. And even when someone generates a fractal with the help of computer, he or she neither invents or creates it. It is always a discovery of something that always existed - somewhere...



An "unorthodox" fractal tree, where the scale remain the same. In this example there are only 5 generations of the branch, but eventually the tree would grow to an infinite size.


A more natural fractal tree, where the branches get smaller and smaller; this is what happens in real trees. This tree grows 7 generations of the branch. With this resolution the next generation would not be visible anymore.


The philosophy in fractals

With computers we can display "perfect" fractals, which means that the patterns repeat in them infinitely. This means that we can zoom a detail of the fractal for ever and always find the same shapes! Depending on the complexity of the formula, we can "travel" through several different forms before coming back to the original - but it's always there.

What's more, we never know what we can find "inside" a fractal when we go in to explore it. For example, in the Mandlebrot set there is a detail called "the valley of seahorses"... and when you zoom into the neck of a "seahorse" eventually you find the original "apple man" shape - and from that you can find the seahorses again!

A fine detail of the Mandelbrot set, where in the middle you can see the repetiion of the original "apple man" shape (look at previous page).

You can explore the Mandelrot in the web at "http://i30www.ira.uka.de/~ukrueger/fractals/html/S0.html".

This, in addition to the sheer beauty of them, is what makes fractals so fascinating. They help us to understand such concepts as infinity and creation of complex shapes out of simple elements. Many scientist also see that they help us get closer of understanding the nature - and the universe itself.