@0bacad63 - the sets do converge as the degrees get large (i.e. the degrees plus 1 get large in a multiplicative sense) , but a lot has not been proved about what the limiting set looks like!   

It's known that this set is contained in the annulus 

1 ≤ |z| ≤ 2 

and that it contains the annulus

2^(-1/4) ≤ |z| ≤ 2^(1/4)

It's also known that this set is connected and locally path-connected!  But that's about all.