Question

Find the first three output values of the fractal-generating function f(z)=z^2-3+2i

Answer 1

Presumably, you would start with a given initial value which can generally be chosen to be
`z_0=x+iy`. Then you would find
`z_3=f(z_2)=f(f(z_1))=f(f(f(z_0)))`. Symbolically, this expression will become quite cumbersome after just the first iteration.

So let's say
`z_0=1`. Then we have


`z_1=f(1)=(1)^2-3+2i`

`z_1=-2+2i`


`z_2=f(-2+2i)=(-2+2i)^2-3+2i`

`z_2=-3-6i`


`z_3=f(-3-6i)=(-3-6i)^2-3+2i`

`z_3=-30+38i`