How does tetration work for base 3 + i ?
I looked at some posts and there was talk about parabolic fixpoints and perturbated (parabolic) fixpoints. And stuff about merging in some way. The number of people involved in those threads and/or the number of posts was low, so I suspect im not the only one with questions ...
Apart from the Shell-Tron region I fail to see the connection of base 3 + i with parabolic fixpoints or perturbations... and maybe there is none ( intended ).
There was some stuff mentioned for complex bases involving riemann mappings and fourier series.
It seems related to Kneser , but its unclear what is mapped where , and why.
pseudocode is nice , but without explainations its " mystic " to the big audience I think.
Also a dead link does not help ofcourse.
W're are talking about analytic tetration , not just continu right ?
I know having more than one fixpoint prevents an analytic solution that agrees on both fixpoints. I dont know how that makes sense then, for kneser we mapped to the real line ... because we wanted real-valued tetration for real bases. But what do we want and do with complex bases ?
Sorry if I have forgotten stuff posted many years ago, I feel a bit like a noob now.
Then again I cannot imagine a young new member/reader without a degree in dynamics too fully understand this from the first time (s)he reads it ...
regards
tommy1729
I looked at some posts and there was talk about parabolic fixpoints and perturbated (parabolic) fixpoints. And stuff about merging in some way. The number of people involved in those threads and/or the number of posts was low, so I suspect im not the only one with questions ...
Apart from the Shell-Tron region I fail to see the connection of base 3 + i with parabolic fixpoints or perturbations... and maybe there is none ( intended ).
There was some stuff mentioned for complex bases involving riemann mappings and fourier series.
It seems related to Kneser , but its unclear what is mapped where , and why.
pseudocode is nice , but without explainations its " mystic " to the big audience I think.
Also a dead link does not help ofcourse.
W're are talking about analytic tetration , not just continu right ?
I know having more than one fixpoint prevents an analytic solution that agrees on both fixpoints. I dont know how that makes sense then, for kneser we mapped to the real line ... because we wanted real-valued tetration for real bases. But what do we want and do with complex bases ?
Sorry if I have forgotten stuff posted many years ago, I feel a bit like a noob now.
Then again I cannot imagine a young new member/reader without a degree in dynamics too fully understand this from the first time (s)he reads it ...
regards
tommy1729