1. Introduction

In the past books like [1] presented recipes to create interesting random patterns using physical phenomena. More recently programs like fractint [6] can create innumerable images by using fractals. If you look more in detail on how those images are produced, you have mainly the following origin [4]:

• Complex maps like the famous Mandelbrot set .
• Systems of differential equations from the theory of dynamical systems.

It seems that only people expert in those two fields can discover interesting new formulas. For example the algorithm corresponding to the Mandelbrot set is:

How can you discover the magical coefficients if you don't know the algebra of complex numbers? The starting point for the method proposed here is the possibility that the algorithm (1) is more fundamental than the complex formula from which it comes (or the system of differential equation). A computer with only the ability to execute the four algebraic operations can create any fractal. This would be in the end a algorithm like (1) with only algebraic operations which is repeatedly executed .