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+--- Thread: My introduction and Some Approximations of Kneser Tetration on Desmos I made (/showthread.php?tid=1822)
My introduction and Some Approximations of Kneser Tetration on Desmos I made - RaeesHarris - 07/07/2026
Hello! My name is Raees. I have been researching tetration and hyperoperations for 5 months. I am currently studying in High School. My birthday is July 2nd. I was born in India. My Hobby is currently researching Tetration and Hyperoperations(since there is so much to explore!) and making numerical models of functions in Desmos. I am mostly self-taught in math.
Anyways, I have tried to make some implementations of Kneser Tetration for Complex heights and a fixed base on Desmos(specifically the function sexp(a+bi), with the data computed using PARI/GP and the program fatou.gp made by sheldonism):
https://www.desmos.com/calculator/hsjtrcgqgs (Test Version to check my idea, works for imag(x) ∈ [-5,5], base e)
These are the Current Versions for a variety of Bases(which technically works for all complex numbers, but i reccommend the real part staying low ):
https://www.desmos.com/calculator/n1prudguef (Current version, base 1.5)
https://www.desmos.com/calculator/anektsk1pb (Current version, base 2)
https://www.desmos.com/calculator/d4frqmds2e (Current version, base 2.5)
https://www.desmos.com/calculator/otrjcsnhoe (Current version, base e)
https://www.desmos.com/calculator/rwfsrv1lte (Current version, base 3)
https://www.desmos.com/calculator/dtvyzocshm (Current version, base Pi)
https://www.desmos.com/calculator/8jbdph3pgv (Current version, base i(I'm not actually sure if its Kneser, i got the data from fatou.gp made by sheldonism))
I also made another approximation for real heights and bases ∈ [1.5,3.5]: https://www.desmos.com/calculator/12qaelj9vz(data computed from fatou.gp)
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My current goal is to make Kneser Tetration for a lot of bases in Desmos. I discovered a path were I think i could achieve an approximation of Kneser tetration(but I need to research and refine my method, also a little sneak peak into the method: https://www.desmos.com/calculator/wonk57usxr).
Feel free to ask me any questions about my approximations of Kneser Tetration on Desmos!(also I am known as DubiumTetration on Reddit, and i uploaded one of my graphs on reddit:"https://www.reddit.com/r/desmos/comments/1tzgjnl/kneser_tetration_for_base_e_for_complex_heights/")