2.2.4 Characteristics - A Fractal is Developed through Iterations/h3>

Self-similarity, as described before in this chapter, can be produced by iterations, which means that certain kinds of formulas or geometric principles are repeated on the previous result of the calculation or drawing respectively. Examples for geometric rules make up the fern and the Koch curve; those for fractals based on a mathematical equation produce the Mandelbrot set.

A film-camera and a television viewer in a dark room can illustrate feedback, which is a phenomenon that is produced by iterations - iterative processes are a main source for complexity. The distance should be about one meter and the cut, which is filmed, should be a little bit larger than the screen. What we then can see is an endless picture of the screen on the screen on the screen ... Now the camera is turned a little bit out of the axes. At one point the screen begins to flash. The light, which is sent out by the glowing phosphor-layer of the television viewer, is met by the lens of the camera; this produces flickering electric streams. A cable leads the electric signal to the screen where it makes some more phosphor glow. Then the next iteration starts. Depending on the adjusting knobs, like for brightness, different things may happen. Some patterns, which can then be seen on the screen, are really constant, even if a hand is held between the screen and the camera or the light is turned on and off, which means that similar pictures will again be produced only after a short time[01].

Footnotes

[01] There are different kinds of behavior to be seen on the screen:
1. If the brightness of the screen is low and the light in the room is shortly turned on, the thus produced pattern disappears and the screen remains dark.
2. If the brightness of the screen is increased, sometimes a short flash is produced which turns into a constant or pulsating pattern.
3. Depending on the adjustments - sharpness, focal length, ... - the pattern is never stabilized and the light moves around the screen before it disappears, then a new flash dances again around the screen and disappears ... The sequence is never or sometimes only after a long period repeated.
4. Depending on the adjustments sometimes a spontanous flash produces "organic" structures, moving patterns with a highly complex spatial structure.
The first and second possibility has too much and the third too little "order". The fourth kind produces interesting patterns with self-organisation. Peak David, Michael Frame, Komplexität - Das gezähmte Chaos (1995), Birkhäuser Berlin, ISBN 3-7643-5132-2, p.22-29.