Iterated maps are produced by putting a number through a function then taking the result and putting it through the equation again, then repeating. Just pick any starting value and keep pressing the cos button. The series of numbers will eventually approach a stable point and there will be no more changes. The stream of numbers is called an 'orbit', the final point is called a stable fixed point. This exercise shows what an iterated map is, however it is a very dull example of an iterated map.
Iterated maps are what many fractals are made of.
The Mandelbrot set is just an iterated map in the complex number plane. Here we will deal with simple one dimensional maps, because they are easier to study. If you wish to study more complex maps, the links page has several fractal links which may or may not attack the subject from a mathematical standpoint. Many fractal sited are dedicated to fractal art. The Logistic Equation A particularly interesting, and popular iterated map is the logistic map.