f(s),h(s) and "hairs".

[tommy1729]

Ok sorry I was not clear enough.

A hair is a shape.

So for instance let tet(s) be analytic tetration.

a = tet(1 + i) 

then consider for r > 0 : exp^[r](a).

this is a continu curve in the complex plane.

Now arctet(exp^[r](a)) = 1 + i + r.

This is a flat line with starting point 1 + i.

the SHAPE of that flat line with starting point 1 + i is a flat line starting at 1+i.
so the hair ( of exp^[r](a) with respect to tet(s) ) is this flat curve.

NOW FOR A GENERAL APPROXIMATION OF tetration f(s) we consider

hair = shape ( inverse_f(exp^[r](s_1)) ).

SO a hair is the shape (not the function and not the values of ) of h(s) where 

f(h(s)) = exp(f(s)).

That is what I meant with : " If f(s) was exactly tetration those paths would be flat and parallel to eachother "
I hope this clarifies.

regards

tommy1729