Fractals

In the 20th century, scientists like Benoit Mandelbrot invented a way to visualise the mathematical phenomenon of complex numbers.

Chaos Theory and the Butterfly Effect

There is also a philosophical aspect to the theory of fractals, the issue of complexity and indetermination. This has also been called the chaos theory, or more poetic, the so called butterfly effect. Two popular examples were cited in every other textbook. If you measure the coast line of Britain, you will end up with a certain length. But if you measure again more accurately every rock and every carving, you will measure a much greater length. In theory, one could say, Britain has an infinite coastline. While this might be no useful knowledge for practival geography. But it might help to understand what happens in modern physical and biological research. The second example states that the movement of a single butterfly in Europe could alter the movement of the air in a way that will, after a chain reaction of small changes which in turn cause greater changes, finally result in a storm over china. This example is similar to traditional Asian stories that teach Buddhism and Tao. After reading popular magazine articles about the chaos theory, many people started to quest for a deeper meaning beyond mathematics and physics. Some people went so far as to presume that there must exist special kinds of fractals which allow scientists to encode subconscious messages within them, so called subliminal fractal information. While this hypothesis has not yet been falsified, it is most unlikely to be true, like so many other popular misconceptions about complex scientific theories. Anyway, fractal images have already served as an inspiration to artists all around the world, and maybe they have also made science and scientific studies a little bit more popular. Surely the example of the butterfly effect has led to more consciousness about global thinking and world ecology

Putting Fractal Theory to Practise

So what are fractals actually useful for? Like mentioned above, they are basically a visualisation of mathematical theory. The visual images can be used in graphical tools for generating patterns, like it is done in various plugins for Photoshop.

Fractal formulae can also be used in landscape simulation, to generate seemingly organic shapes like those of hills and mountains, hair and vegetation (plants). Look at software like Bryce for example, or classic computer games like Rescue on Fractalus.

In the 1980s, it could take several hours to calculate a fractal by the size of 320 x 200 Pixels on a Commodore 64. Even when more sophisticated computers like Amiga, Atari ST and Apple Macintosh made fractal generation, 3D graphics and raytracing finally available to a public audience, it still took high-end workstations to produce animated computer graphics of higher quality like the famous Pixar trailers. Nowadays, fractal landscape generation plays an important part in the making of visual effects for action and fantasy films.

Julia Sets and the Famous Apple Shape

Fractum in latin means a part, as opposed to totum, the whole. So fractal in its literal meaning is the opposite of total. Usually, the word fractal refers to graphical representations produced by using fractal theory.

In German, the term Apfelmaennchen (little apple creatures) used to be quite common to decribe certain apple like shapes produced by fractal graphic programs. These are variations of the Julia set. They have only been discovered in 1979 by scientist Benoit Mandelbrot. This famous object has been printed in books and magazines in different and often colourful variations. This is what the basic shape looks like: