Patent ID: 6894705

Claim:
A computerized method for creating an image dependent upon a polynomial equation, the steps comprising: a) providing a predetermined polynomial equation; b) approximating at least one root of said polynomial equation by performing at least one of an infinite number of iteration functions that is represented as {B m (z)} m ∞ , wherein B m (z) represents a fundamental family of iteration functions called the “Basic Family,” m is a natural number ranging ∞≧m≧2, and z is a complex number representing an input or variable, whereby each Basic Family member will visualize any polynomial equation in a different manner to produce unique images even if applied to the same polynomial equation; c) selecting either one or any combination of said Basic Family of iteration functions to produce graphical images based upon said polynomial equation; d) generating a graphical image as a function of the selected Basic Family member or members and said at least one root of said polynomial equation; and e) colorating said graphical image to produce an initial color rendition thereof.