Source=http://www.student.wau.nl/~hylke/fractals.html

# The Mandelbrot and Julia Sets

### Back to the Mandelbrot set, how is it created?

Pick a complex point. Say you pick
0.5 + 0.75 i. It is labeled z0. Locate it on the graph.

The next point is z1. It is approximately 1.3125 + .96 i. We get this point by squaring the complex number, 0.5 + 0.75 i, and adding the result to the original number. This process can be written as a function, z1 = z02 + z0.
Now, to get z2, we square z1 and add it to z0.
The iteration process continues: z0, z02 + z0, (z0 2 + z0)2 + z0, ((z0 2 + z0)2 + z0)2 + z0, ...

### We can write it as a recursive function zn+1 = zn2 + z0.

Notice how z3 is far away compared to the other points. It appears that this, z0 was not a good choice to be in the Mandelbrot set, since after 3 iterations, it moves out. Good choices are numbers that stay "nearby" after n iterations. People who study this set find that it fits inside
the square -1.2 < x < 1.2 and -2 < y < 0.5.

### Try out some for yourself. Next page.

Want to go back ?
Wait! More review of complex numbers needed.