new fatou.gp program

[sheldonison]

Dear Sheldonison,
Your PARI/GP code is an invaluable resource for tetration research. Do you have any plans to update it further? I noticed the algorithmic complexity is \(O(P^3)\) , which makes it quite difficult to work with precision in the thousands of digits due to the cubic scaling in computation time. While it’s fast enough for a few hundred digits, high-precision tasks require a lot of time and processing power.
Respectfully yours,
Pentalogue Tridecalogue.

Hi Pentalogue,
Thank you for your kind words.  I may return to my tetration hobby now that I am retiring from being a processor development engineer at IBM.  As far as the convergence rate of  \(O(P^3)\), I assume that you are correct .  I have no idea  how to improve fatou.gp, though I may revisit the algorithm and try to move it to other more modern platforms like python, but that is a very long term goal.  First I want to get some education on math.  I self taught myself all this graduate level complex dynamics stuff but I need to fill in the gaps that a normal BS math major would have learned....