How are the Julia and Mandelbrot sets computed?
The process is rather similar. It has been explained previously that the Mandelbrot set iterates z2+c with z starting at 0 and varying c when the Julia set iterates z^2+c for fixed c and varying starting z values. The question is how to stop the iteration. It can be demonstrated that if |z|>2 the value will always escape towards infinity: then, iteration can be stopped for this point. |z| is the square root of x2+y2 and is named the modulus of the complex number. 2 is the bailout value for the Julia and Mandelbrot sets. When using a large enough number of iterations (at least one or several hundreds for each point), it can be assumed that almost all the points with |z|<2 pertain to the set (there is a small uncertainty for a few points near the border of the set, and the higher the number of iterations is, the better the precision of the image is). Other polynomials need other bailout values, but interesting images might be obtained with bailout values lower than the theoretical one. I
