What is the Mandelbrot set?
The Mandelbrot set is clearly related to the Julia set z(n+1)=z2(n)+c but you must distinguish what is different. Now cis not a constant, but a variable, and the set is drawn in the plane defined by the real and imaginary values of c (the Mandelbrot set is drawn in the c plane when the Julia set is drawn in the zplane). For each point c of the plane, the polynomial is iterated, starting at the critical point z=0 (during each iteration for a given point, only z changes, not c; when the result is obtained, the polynomial is iterated for the the next point c of the plane, starting again with z=0).
