Natural complex tetration program + video

[MorgothV8]

I've created this:
https://www.youtube.com/watch?v=XVT1thcH...e=youtu.be

Code is here: https://github.com/lukaszgryglicki/jpegbw

This video shows complex natural tetration with contour lines defined here: https://github.com/lukaszgryglicki/jpegb.../varinc.sh

0<=t<=1 changes while video plays. There are 1000 frames, so on 645 frame, t=0.645.
Real contour line is: exp(8*(t-0.5)-exp(8*(t-0.5)), so ranges from very low negative to very high positive number.
Real line is red, values higher contour are light red, values lower than contour are light teal.

Imag contour line is: exp(8*(t-0.5)-exp(8*(t-0.5)), so ranges from very low negative to very high positive number.
Imag line is blue, values higher contour are light blue, values lower than contour are light yeallow.

Modulo/Abs contour line is: exp(8*(t-0.5), so ranges from very low positive to very high positive number.
Modulo line is green, values higher contour are light green, values lower than contour are light pink.

All colours are blended, so light gray means that all: real, imag and modulo are lower or higher than their contours.
Other combinations possible.

Tetration code is here: https://github.com/lukaszgryglicki/jpegb...ster/tet.c
Drawing code is here: https://github.com/lukaszgryglicki/jpegb...ap/cmap.go
Function parser is here (user can provide functions as strings): https://github.com/lukaszgryglicki/jpegb...er/fpar.go

[MorgothV8]

My question is (maybe someone can help).
How can I make it more general?
This version caculates tetration base "e" and uses a lot of special tables and exp fixed points constants.
Probably all those tabular values are derived from exp fixed points somehow.

I know that there are two non-real fixed points for exponentials with bases >= 1^(1/e).
For bases from 1^-e to e^(1/e) there are real fixed points...

But can *anybody* give me a formula to calculate fixed points of any exponential with base beeing real number >= e^(1/e)?
And then how to derive all those tabulart values and algorithms for such bases?

I guess all code would be totally different for 1^-e to e^(1/e) cases, not even mentioning bases < e^(-e) or (sic!) ANY complex bases?