What are the types of complex iteration and tetration?

[Daniel]

I'm pulling together a Mathematica notebook to submit to the Wolfram Function Repository and was thinking to name it ComplexIteration. With so many approaches here focused on real tetration I wonder if there are other approaches to complex iteration and tetration besides mine. Gottfried's work with matrices is the closest to my work that I know of, but then at least some approaches to real tetration start with employing complex tetration. All these approaches need to be consistent or derived from Schroeder's functional equation and the math is comparatively simple (for this forum), so I wouldn't be surprised if different approaches to complex tetration lead to the same place.