Question

What are the rules for behaviours of quadratic iterations?
For the iteration of Z to Z^2 what effect does the starting point have?
What causes it to be chaotic, invariant, cyclic (1,2,3,n), divergent and convergent?
Any help is appreciated thanks!

Answer 1

iterations of duadratic? like x^2 +y^2 + z^2 + ..?

or:

x^0 + x^1 + x^2 +x^3 + x^4 + ...

Answer 2

duadratic means.... a cant type quadratic none to gooder

Answer 3

Thanks for replying!!
Ummm its not even that complicated.
We are just looking at what happens to a complex number, Z, as we sqaure it. That is the iteration.
I already found out that if the length of z0 (initial value) is less than 1 it will converge and if it is greater than 1 it will diverge. Also if z0=zn it will be invariant. But I dont know about the others. :S