Help : Triternion Hyper Parameter TMan

Hi All,
I'm working on a new game The formula is TMan in Russell Walsmith orgform.
Basically is my SlopeTMan that i'm rewritng and re-structured but i have a problem.
I have implemented the TMan of Russell and i added also a normal Mandelbrot that i attach under.
In your opinion is it correct?
That parameter is correct?
Try it to p1 (0.0 , 0.1), you will see the black line, i think is missing of something but i don't understand what.

The set is correct

  x2 = x * x - y * y - z * z + cx;
  y2 = 2 * x * y + cy;
  z2 = 2 * x * z + cz;

This is the formula

TMan{
  c1=real(pixel)
  c2=imag(pixel)
  c3=p1
  z1=z2=z3=0

  :

  t1=z1^2-z2^2-z3^2
  t2=2*z1*z2
  t3=2*z1*z3
  z1=t1+c1
  z2=t2+c2
  z3=t3+c3

  z=z1+z2+z3
  |z| < 64
}

At the end i don't find any solution, or better i can change planes using c3 but the corret loop i think is this.
Some suggests are appreciate, the question is PARAMETER 1 is working correctly? I think yes.
Suggests?

TMan{
  z1=z2=z3=0
  c1=real(pixel)
  c2=imag(pixel)
  c3=p1

  :

  t1= z1^2-z2^2-z3^2
  t2= 2*z1*z2
  t3= 2*z1*z3

  z1=t1+c1
  z2=t2+c2
  z3=t3+c3
  z=z1^2+z2^2+z3^2

  |z| < 64
}

Hi, i understood the problem, because basically that set is a 3D Quat, the parameter 1 work correctly in the real part and in a normal Quat, the real and image part of cj ck are the same, you can see it in fractint colletion, quaternion mandelbrot, instead in this version the real part is ok but the image part is creating that black line but only in p1=(0.0,0.1) so using image part at 0.1, or 0.2,0.3 using the image part, the solution can be add a low value at zk and UF does the iteration and the black line disappears.
BTW next days i'll upload the formula on the DB so you can see it, SlopeTMan, i wanted upload it here before that in the UFDB but i think i can't because i tried yesterday but the formula is 2240 lines and i think exceeds the maximum lines allowed in a post, because is trunked.
Ciao a tutti e buon week-end

TMan{
  z1=z2=z3=0.0
  pk=1e-3
  c1=real(#pixel)
  c2=imag(#pixel)
  c3=p1

  :

  t1= z1^2-z2^2-z3^2
  t2= 2*z1*z2
  t3= 2*z1*z3+pk

  z1=t1 + c1
  z2=t2 + c2
  z3=t3 + c3
  z=z1^2+z2^2+z3^2

  |z| < 128
}

Resolved....
This is a solution, but yes there is nothing of wrong, just decide how parameter 1 must work or better, image part of parameter 1.
This is a solution but i don't know if i will use this solution or the solution added a low value to p1, because in my formula there are also other combinations, there are 4 hyper complex parameters, this is just one. But there is nothing of wrong.
BTW this is a solution, p1 now works correctly like as Quat Mandelbrot in fractint collection.

TMan-C{
  zr=0
  zi=0
  zk=0
  c1=real(#pixel)
  c2=imag(#pixel)
  c3=p1

  :

  zkr=real(zk)
  zki=imag(zk)
  t1= zr^2 - zi^2 - zkr^2 - zki^2
  t2= 2*zr*zi
  t3= 2*zr*zkr + flip(2*zr*zki)

  zr=t1 + c1
  zi=t2 + c2
  zk=t3 + c3
  z=zr+flip(zi)

  |z|+|zk| < 128
}

No guys nothing done, I have decided that in the new SlopeTMan I will not put the normal Mandelbrot Set because I don't like how it works, in the formula there are also the variations of the planes the 3D dimensions and if the Triternion is not composed correctly, changing the planes , hyper complex parameters behave incorrectly. Using Russell's TMan the structure is correct and all the parameters work correctly if I try to insert a normal Mandebrot it does not work as it should so the setting is wrong, in fact I was just exploring possible sets.

Hi,
At the end i must share the formula, i attach the link where you find as2.ufm + SlopeTMan, i renamed in asNew for comfort when uploading from UF, here there is SlopeTMan.
There is for sure the Triternion Mandelbrot changing C , but i wanted add also a normal Mandelbrot but with this structure is not so simple.
The formula is good and the 3R dimension are very usefull.
Ciao a tutti

https://fractalcosmo.com/as2New.zip

Hello everybody,
Well, after days of studying I found that the cjk parameter, i.e. hypercomplex, works well with the set

t1 = z1 ^ 2 - z2 ^ 2 - z3 ^ 3
t2 = 2 * z1 * z2
t3 = 2 * z1 * z3

I found an example in gnd, you can see that the work of cjk is that, even if it puts this black space that I really don't like, there are several solutions but we must also see how the hypercomplex works by changing the "variation" ( plans). So it seems standard but there is something that does not convince me.
I uploaded the formula to my folder on my site, I entered a Select Formula operator, you can see that by putting formula 2 and cr | ci | ck in select C we have mandelbrot then the Hyper Param 1 is what I am studying, but there are also plans to analyze.
For the moment it remains in private and in as2.ufm I leave the one I uploaded, because in Russel's formula and floors z1, z2 and z3 are well structured within the 3 dimensions and therefore even changing the floors and hypercomplexes everything works well while with the normal Mandelbrot then the above equation there is something that does not convince me.
Before downloading I recommend doing a cache cleanup, in my site the folder will be called as2New.ufm so as not to conflict with as2.ufm in the database.

Here's the link :

https://fractalcosmo.com/as2New.zip