Newton's Method by Adrian Porter

pics
code

In this project, I took an equation that was quite different from the mendelbrot and applied it to the fractal shell.

Z is a complex number
The equation is Z(n) = Z(n-1) - F(Z(n-1)) / F'(Z(n-1))
Z(0) = any number (for the pictures Z(0) = x + yi)
F is the function and F' is its dirivative:
F(i) = i ^ p - 1 where p is a power.
we can calculate F' using the power rule:
F'(i) = p * i ^ (p-1)

to do this with complex numbers see how

what happens is the program calculates Z(1) and sees if |Z(1)| is close to the answer. If it isn't, then it calculates Z(2), and Z(3) . . .
It picks a color depending on how long it took. If it takes a real long time, then it colors it black