In the past books like  presented recipes to create interesting random patterns using physical phenomena. More recently programs like fractint  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 :
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 .