The Mandelbrot Set
Where does the color come from?
We know the points in the set are coded black. The Java applet you will see took the
function out to 100 iterates. After n iterates, the point may leave the set proceeding
on its way to infinity. If n is a small number, then the point goes out to infinity
very quickly. If n is close to 100, then the point's orbit, or iterate path, stays
inside the set for awhile before it leaves.
Let's take our earlier example, z0 = 0.5 + 0.75 i. This appears to have left
the set after the 1st or 2nd iterate. We can check this by finding the
distance from z2 to the origin. How do we compute distances between two complex
numbers? Look it up. If the result is greater than a radius of 3,
then the point has left the set. Since n = 2, it would be assigned the color for 2, say
it is purple.
Go on to the Julia set.
To see the Mandelbrot and Julia sets, go into the java
Want to go back ?
Back to other activities.