What are iterated complex polynomials?
Complex polynomials are used to draw the well known images of Julia and Mandelbrot sets. The first researches about iteration of complex polynomials were those of Julia (1918) and Fatou (1919-1920). In spite of the fact that Julia’s name is the most known among the world of fractal artists, the works of Fatou, which were developed independently, are closely related and complementary. Let us consider the simple polynomial: z2+c where c is an arbitrary constant and z is a variable. Moreover, z and c are complex numbers (see section 4). Now we write z(n+1)=z2(n)+c and start, for example, with z=0. This means that the first value of the polynomial (at the first iteration, i.e. when n=1) is c. Now, for the second iteration (n=2), the value of z is c; the result of the first iteration and the polynomial has now value c2+c. The polynomial will be iterated endlessly, giving to z, at each time, the value of the polynomial computed in the previous iteration. To understand why this computation ca
