tetration from alternative fixed point

[sheldonison]

Kouznetsov's method requires three consecutive exponents, (he uses 0, 1, e), and their vertical (along increasing imaginary) paths to the fixed point.

As I think a second time about it, why does he need paths to the fixed point?
He integrates along the paths Re(z)=1, Re(z)=-1.
He merely forces the value of the superfunction to be the fixed point for imaginary part going to infinity. How the path behaves while going to the fixed point is not essential for his computation, isnt it?

After reading the cauchy computation thread, I think the Cauchy algorithm is sensitive to getting a reasonable initial guess that is close enough to get convergence, and is also sensitive to updating the nodes in in an order that helps guarantee convergence.

Are there any links on the forum with Riemann (Knesser's solution) mapping results? I remember Jay posted some results. I've been toying with very simple iterative Riemann mapping, and was able to get some semi-reasonable results.