Question

I'm really at a dead end here guys, any help is massively appreciated....
For the iteration of Z to Z^2 what effect does the starting point have?
What are the rules for behaviours of quadratic iterations?
What causes it to be chaotic, invariant, cyclic (1,2,3,n), divergent and convergent?
Basically Z is any complex number and the iteration is to square it.
So if Z0 (initial point) is 1 (1+oi) then we would sqaure it. Then sqaure that answer. Then sqaure that answer. And etc.
Obviously in that case it is invariant but I dont know what causes it to be chaotic or cyclic..
Any advice please!