https://tetrationforum.org/ Tue, 11 Aug 2026 10:30:34 +0000 MyBB https://tetrationforum.org/showthread.php?tid=1822 Tue, 07 Jul 2026 13:22:44 +0000 RaeesHarris]]> https://tetrationforum.org/showthread.php?tid=1822
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 sheldonison))

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)

_________________________________________________________________________________________________________________________________________________

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/")]]>
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 sheldonison))

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)

_________________________________________________________________________________________________________________________________________________

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/")]]> https://tetrationforum.org/showthread.php?tid=1811 Mon, 20 Oct 2025 15:28:21 +0000 Gottfried]]> https://tetrationforum.org/showthread.php?tid=1811
 it is about 6 weeks, that some correspondent from USA told me he cannot access the files on my website. It seemed so as well from Scotland - but the access from Germany seems to work (I can access everything by ftp:// and even by https:// ).
Now the admin of our small network https://helms-net.de tells me he had tried to reverse some changes he had made in spring, and I would like to check, whether international folks can now access my work again.

Could someone please try to access my math-homepage  

        https://go.helms-net.de/math/tetdocs/index.htm

and if that is possible, then to download just a single *.pdf-file as test?

Please tell me the result here, or even better, mail me at

     mailto:gottfried.helms@t-online.de

(possibly include the error-message as well)


Thank you in advance -

Gottfried.]]>
 it is about 6 weeks, that some correspondent from USA told me he cannot access the files on my website. It seemed so as well from Scotland - but the access from Germany seems to work (I can access everything by ftp:// and even by https:// ).
Now the admin of our small network https://helms-net.de tells me he had tried to reverse some changes he had made in spring, and I would like to check, whether international folks can now access my work again.

Could someone please try to access my math-homepage  

        https://go.helms-net.de/math/tetdocs/index.htm

and if that is possible, then to download just a single *.pdf-file as test?

Please tell me the result here, or even better, mail me at

     mailto:gottfried.helms@t-online.de

(possibly include the error-message as well)


Thank you in advance -

Gottfried.]]> https://tetrationforum.org/showthread.php?tid=1805 Sat, 30 Aug 2025 14:08:42 +0000 Alex Zuma 2025]]> https://tetrationforum.org/showthread.php?tid=1805 my birthday: january 21, 2008
gender: male
pronouns: he/him/his
i was born in romania and i live in romania.
i like video editing, gameplays, advanced mathematics, and googology.
i also like to create graphs on desmos.
a few graphs i made on desmos:
base e hyperoperations: https://www.desmos.com/calculator/ueqda2tbk8
base 2 hyperoperations : https://www.desmos.com/calculator/q3gbpkftz8
base 10 hyperoperations : https://www.desmos.com/calculator/vz8uwgwgql
base 3 hyperoperations : https://www.desmos.com/calculator/l4i9w4b2am
base 4 hyperoperations : https://www.desmos.com/calculator/mevebbamf9
base 1.7 hyperoperations : https://www.desmos.com/calculator/dl1usyacyw
base 1.5 hyperoperations : https://www.desmos.com/calculator/wluijn05la
the cheta function: https://www.desmos.com/calculator/ypj0mvflmd
the xth super root of 2: https://www.desmos.com/calculator/akhnu1rpxo
the xth super root of x and infinite pentation: https://www.desmos.com/calculator/heiz8lyy3u
half tetrations: https://www.desmos.com/calculator/aettjlb2qp
the tetration of the square root of 2: https://www.desmos.com/calculator/qyhpxmyieu
tetration base eta: https://www.desmos.com/calculator/8obpqlvmwo
half-exponential function approximated by a polynomial: https://www.desmos.com/calculator/kb813o3cdx
the tetration of pi: https://www.desmos.com/calculator/udxupmmygc
i hope you enjoy seeing these graphs as much as i enjoyed making them!]]> my birthday: january 21, 2008
gender: male
pronouns: he/him/his
i was born in romania and i live in romania.
i like video editing, gameplays, advanced mathematics, and googology.
i also like to create graphs on desmos.
a few graphs i made on desmos:
base e hyperoperations: https://www.desmos.com/calculator/ueqda2tbk8
base 2 hyperoperations : https://www.desmos.com/calculator/q3gbpkftz8
base 10 hyperoperations : https://www.desmos.com/calculator/vz8uwgwgql
base 3 hyperoperations : https://www.desmos.com/calculator/l4i9w4b2am
base 4 hyperoperations : https://www.desmos.com/calculator/mevebbamf9
base 1.7 hyperoperations : https://www.desmos.com/calculator/dl1usyacyw
base 1.5 hyperoperations : https://www.desmos.com/calculator/wluijn05la
the cheta function: https://www.desmos.com/calculator/ypj0mvflmd
the xth super root of 2: https://www.desmos.com/calculator/akhnu1rpxo
the xth super root of x and infinite pentation: https://www.desmos.com/calculator/heiz8lyy3u
half tetrations: https://www.desmos.com/calculator/aettjlb2qp
the tetration of the square root of 2: https://www.desmos.com/calculator/qyhpxmyieu
tetration base eta: https://www.desmos.com/calculator/8obpqlvmwo
half-exponential function approximated by a polynomial: https://www.desmos.com/calculator/kb813o3cdx
the tetration of pi: https://www.desmos.com/calculator/udxupmmygc
i hope you enjoy seeing these graphs as much as i enjoyed making them!]]> https://tetrationforum.org/showthread.php?tid=1803 Tue, 10 Jun 2025 14:20:10 +0000 Pentalogue]]> https://tetrationforum.org/showthread.php?tid=1803 My apologize, I wrote my self-introduction here because there is no option to do so in the Community.

Introduction 2025.06.10
Hello people! I'm Pentalogue
My birthday: October 11th
Gender: Male
Pronouns: He/Him/His
I born and live in Russia
Fact:
I'm a lover of electronic music (techno, EDM, trance, house, dubstep, d&b, "growling", ambient), jazz, symphonic, classical music and all sorts of quirky and testing sounds. I study music theory, sound theory and sound processing techniques. I am an budding music and MIDIs creator. As of late, I am now also a fan of normal and black MIDIs.
I also enjoy mathematics, studying number theory, mathematical functions, including those rarely mentioned in maths. I am interested in googology, I like big numbers. I'm into creating graphs on the Desmos website.

I joined this community quite recently and want to understand everything that is happening here and what answers users give to questions regarding the main topic of this forum. As I have noticed, it is quite quiet (deserted) here, and no one has been discussing this complex topic for quite some time.]]> My apologize, I wrote my self-introduction here because there is no option to do so in the Community.

Introduction 2025.06.10
Hello people! I'm Pentalogue
My birthday: October 11th
Gender: Male
Pronouns: He/Him/His
I born and live in Russia
Fact:
I'm a lover of electronic music (techno, EDM, trance, house, dubstep, d&b, "growling", ambient), jazz, symphonic, classical music and all sorts of quirky and testing sounds. I study music theory, sound theory and sound processing techniques. I am an budding music and MIDIs creator. As of late, I am now also a fan of normal and black MIDIs.
I also enjoy mathematics, studying number theory, mathematical functions, including those rarely mentioned in maths. I am interested in googology, I like big numbers. I'm into creating graphs on the Desmos website.

I joined this community quite recently and want to understand everything that is happening here and what answers users give to questions regarding the main topic of this forum. As I have noticed, it is quite quiet (deserted) here, and no one has been discussing this complex topic for quite some time.]]> https://tetrationforum.org/showthread.php?tid=1772 Mon, 28 Aug 2023 19:33:16 +0000 tommy1729]]> https://tetrationforum.org/showthread.php?tid=1772
YELLOW ALERT : login issues

made me additionally(!) aware, I have no way to contact you guys !

And very little effort has been made for that.

I invited you all to a facebook but no reactions.

There seems to be no backup contact ways.

community ??


regards

tommy1729]]>
YELLOW ALERT : login issues

made me additionally(!) aware, I have no way to contact you guys !

And very little effort has been made for that.

I invited you all to a facebook but no reactions.

There seems to be no backup contact ways.

community ??


regards

tommy1729]]> https://tetrationforum.org/showthread.php?tid=1718 Mon, 27 Feb 2023 12:03:32 +0000 tommy1729]]> https://tetrationforum.org/showthread.php?tid=1718
Is there a protection ?

roll-back or something ?


regards

tommy1729]]>
Is there a protection ?

roll-back or something ?


regards

tommy1729]]> https://tetrationforum.org/showthread.php?tid=1695 Fri, 27 Jan 2023 22:22:39 +0000 tommy1729]]> https://tetrationforum.org/showthread.php?tid=1695
  1301.3669 combinatorics.pdf (Size: 59.65 KB / Downloads: 455)

  0005008 takeuchi.pdf (Size: 262.47 KB / Downloads: 561)

  1510.05799.pdf (Size: 133.19 KB / Downloads: 551) ]]>
  1301.3669 combinatorics.pdf (Size: 59.65 KB / Downloads: 455)

  0005008 takeuchi.pdf (Size: 262.47 KB / Downloads: 561)

  1510.05799.pdf (Size: 133.19 KB / Downloads: 551) ]]> https://tetrationforum.org/showthread.php?tid=1686 Wed, 28 Dec 2022 07:36:04 +0000 JmsNxn]]> https://tetrationforum.org/showthread.php?tid=1686
Additionally, I have free time, and I like to do math to distract myself. My dad's pretty fucked because his daughter died. It's pretty surreal. So I'm kind of rage posting here; but rage posting math. I apologize if I use language that isn't suited to mathematicians. Please don't take my results for the next week or so as anything more than me being pissed off and trying to deliver results I know. I'm just angry and will post math as a manner of calming down.

I'm okay, don't worry about me. I just need some catharsis of posting random math results. But the manner I will post them will be uncouth. They will be ugly, and aggressive. And I will swear a lot.

I apologize.]]>
Additionally, I have free time, and I like to do math to distract myself. My dad's pretty fucked because his daughter died. It's pretty surreal. So I'm kind of rage posting here; but rage posting math. I apologize if I use language that isn't suited to mathematicians. Please don't take my results for the next week or so as anything more than me being pissed off and trying to deliver results I know. I'm just angry and will post math as a manner of calming down.

I'm okay, don't worry about me. I just need some catharsis of posting random math results. But the manner I will post them will be uncouth. They will be ugly, and aggressive. And I will swear a lot.

I apologize.]]> https://tetrationforum.org/showthread.php?tid=1683 Thu, 22 Dec 2022 16:14:36 +0000 bo198214]]> https://tetrationforum.org/showthread.php?tid=1683  OMG I was trying ChatGPT, seems it is not very advanced yet with respect to tetration 


  snip_20221222171310.png (Size: 82.83 KB / Downloads: 832) ]]>  OMG I was trying ChatGPT, seems it is not very advanced yet with respect to tetration 


  snip_20221222171310.png (Size: 82.83 KB / Downloads: 832) ]]> https://tetrationforum.org/showthread.php?tid=1675 Sun, 04 Dec 2022 11:02:04 +0000 Daniel]]> https://tetrationforum.org/showthread.php?tid=1675 the person to become famous in extending tetration. But over the years and decades I have seen how the development of tetration has been a vast tapestry of people working, that often didn't know each other. I believe that the story of tetration is not that of a single person, but something far more interesting and fun. My sister is an amazing author and I have been thinking about getting her help to write the human stories behind tetration. But I would need to hear peoples stories. Any interest?

There are three ways to support math I can think of - research, education and community building. I hope even if large chunks of my work sucks that my work on furthering the tetration community with do some good.]]> the person to become famous in extending tetration. But over the years and decades I have seen how the development of tetration has been a vast tapestry of people working, that often didn't know each other. I believe that the story of tetration is not that of a single person, but something far more interesting and fun. My sister is an amazing author and I have been thinking about getting her help to write the human stories behind tetration. But I would need to hear peoples stories. Any interest?

There are three ways to support math I can think of - research, education and community building. I hope even if large chunks of my work sucks that my work on furthering the tetration community with do some good.]]> https://tetrationforum.org/showthread.php?tid=1636 Sat, 03 Sep 2022 07:00:09 +0000 Gottfried]]> https://tetrationforum.org/showthread.php?tid=1636
Going with this now many days recently, it came to me that I have this nice wedding-picture at the wall, where my older brother and my sister-in-law had taken a photo and had let it convert to an acryl-painting on linnen having a wooden frame. 
See this:

  20220903_084407.jpg (Size: 93.25 KB / Downloads: 785)  

They gave me the honor of citing a topic of my webpage - namely the halfiteration-thingy. At one edge of this wooden block-frame my then hobby of the challenge of the Erdoes-statement is taken:


  20220903_084437.jpg (Size: 146.01 KB / Downloads: 651)

Seems to be solved now...  

Thanks James for your work!

Community -greetings:

Gottfried]]>
Going with this now many days recently, it came to me that I have this nice wedding-picture at the wall, where my older brother and my sister-in-law had taken a photo and had let it convert to an acryl-painting on linnen having a wooden frame. 
See this:

  20220903_084407.jpg (Size: 93.25 KB / Downloads: 785)  

They gave me the honor of citing a topic of my webpage - namely the halfiteration-thingy. At one edge of this wooden block-frame my then hobby of the challenge of the Erdoes-statement is taken:


  20220903_084437.jpg (Size: 146.01 KB / Downloads: 651)

Seems to be solved now...  

Thanks James for your work!

Community -greetings:

Gottfried]]> https://tetrationforum.org/showthread.php?tid=1635 Sat, 03 Sep 2022 02:13:09 +0000 JmsNxn]]> https://tetrationforum.org/showthread.php?tid=1635 https://tetrationforum.org/showthread.php?tid=1617 Fri, 12 Aug 2022 17:23:36 +0000 Leo.W]]> https://tetrationforum.org/showthread.php?tid=1617 plz feel free to share if you have any interesting graphs (gifs are better!)


for \(exp_e(z)\): (due to some branch cuts there are 2 points in the right and some cuts in the left should be excluded)
p1: \(exp_e^t(z), t\in[-1,1]\)
p2: \(exp_e^{e^{it}}(z), t\in[0,2\pi)\)
p3: \(exp_e^{it}(z), t\in[-1,1]\)
also I have to say that does the iteration to an imag height always tortune and rotate the original function in some manner? at least the photos represent to me with such impression
All these iterations generated by Kneser's tetration.

for \(sin(z)\): 
p4: for real \(z\in[-\pi,\pi]\), plot \(sin^t(z),t\in[0,1]\)
Generated by fixed point method.

  ExpUnit.gif (Size: 7.38 MB / Downloads: 715)

  ExpCirc.gif (Size: 7.96 MB / Downloads: 671)

  ExpImag.gif (Size: 7.61 MB / Downloads: 760)

  Sin2.gif (Size: 272.24 KB / Downloads: 683) ]]> plz feel free to share if you have any interesting graphs (gifs are better!)


for \(exp_e(z)\): (due to some branch cuts there are 2 points in the right and some cuts in the left should be excluded)
p1: \(exp_e^t(z), t\in[-1,1]\)
p2: \(exp_e^{e^{it}}(z), t\in[0,2\pi)\)
p3: \(exp_e^{it}(z), t\in[-1,1]\)
also I have to say that does the iteration to an imag height always tortune and rotate the original function in some manner? at least the photos represent to me with such impression
All these iterations generated by Kneser's tetration.

for \(sin(z)\): 
p4: for real \(z\in[-\pi,\pi]\), plot \(sin^t(z),t\in[0,1]\)
Generated by fixed point method.

  ExpUnit.gif (Size: 7.38 MB / Downloads: 715)

  ExpCirc.gif (Size: 7.96 MB / Downloads: 671)

  ExpImag.gif (Size: 7.61 MB / Downloads: 760)

  Sin2.gif (Size: 272.24 KB / Downloads: 683) ]]> https://tetrationforum.org/showthread.php?tid=1598 Fri, 22 Jul 2022 00:02:55 +0000 Daniel]]> https://tetrationforum.org/showthread.php?tid=1598 Peace, ]]> Peace, ]]> https://tetrationforum.org/showthread.php?tid=1586 Sat, 16 Jul 2022 02:30:59 +0000 Daniel]]> https://tetrationforum.org/showthread.php?tid=1586