Tutorial Chapter 1
What is a Fractal?Imagine flying in a space shuttle looking at the coast of Britain. From such a great distance the coast looks perfectly straight, going from north to south. But, as you approach the earth something tells you the coast is not perfectly straight... Of course! As you go into the upper atmosphere you realize that it has thousands of bays, harbors, capes, and peninsulas that you could not see from a distance. Thinking that now you have a detailed picture of the coast, you turn towards one of the harbor beaches, which seems to be straight... However, as you get closer to it, you see that it too has thousands of smaller bays, harbors, capes, and peninsulas! Wondering if this will ever end you decide to get even closer... Eventually you wind up on the beach looking at the coast through a microscope. You can now see every grain of sand clearly, but, it too has thousands of indentations and extrusions!
No matter how close you get, you will
always see a similarly detailed picture
(maps provided by MapQuest)
The fact that any small part of the coast will look similar to the whole thing was
first noted by Benoit Mandelbrot. He called shapes like this fractals. Fractals are
figures with an infinite amount of detail. When magnified, they donít become more
simple, but remain as complex as they were without magnification. In nature, you can find
them everywhere. Any tree branch, when magnified, looks like the entire tree. Any rock
from a mountain looks like the entire mountain. The theory of fractals was first developed
to study nature. Now it is used in a variety of other applications.
And, of course, beauty is what makes them popular!
|Fractint 19.6 for DOS
One of the best programs ever made for generation of fractals . Includes modules for creating most fractals described on this website, and exporting them into gif images
|Fractint 18.21 for Windows|
Fractint for X-Windows
Geometry of Nature
Benoit B. Mandelbrot
Fractals without this book is like literature without an alphabet. Written by the founder of fractals himself, this book covers a tremendous range of topics and interesting applications. Although it is not very easy to read, you will find a lot of nice pictures and interesting topics even if you don't go deeply into them.