Do z-->z/c² or z-->z*c² create a fractal

[Chillheimer]

I tried to attach it to a message but got: "Your file is too large. The maximum attachment size allowed is 256 KB. "

sorry for that, we currently face major problems with our server and are happy the forum is running at all. working on a solution - until then, please upload externally and share the link here.

[LionHeart]

Thanks Chillheimer.

Let me know when I can attach my program as there may be others who want to play with it

[Chillheimer]

we'll post an announcement as soon as it works again.

until then, why not use a free hoster like https://wetransfer.com/

[LionHeart]

Thanks Chillheimer,

I have not heard of that site. If others have a problem, I'll give it a go.

[LionHeart]

Hi Chillheimer,

It seems to work...

https://we.tl/XgsgNlwBmH

The link will last a week.

Many thanks.

[clacker]

I implemented this function as a Fragmentarium script for the z = (z^n+c)/(c^n+z) function that lets you play with the Julia values and vary the power from -4 to 4.  Here are some samples and the frag file.

[Adam Majewski]

I made it in Ultra Fractal.  Here is the formula.  If you don't use Ultra Fractal, you should be able to read the code and figure it out for the program that you use.  The Mandelbrot version is trickier, since finding a critical point for beginning the iteration is not trivial.


rational-julia {
;
; from pieman597
; http://www.fractalforums.com/general-discussion-b77/t24459/msg95653/#new
;
; based on f(z) = (z^2+c)/(c^2+z)
; generalize to any power
;
init:
  complex bottom=(0,0)
  complex c=@julparam
  complex cton=c^@power
  complex top=(0,0)
  complex z=#pixel
loop:
  top=z^@power+c
  bottom=z+cton
  z=top/bottom
bailout:
  |z|<@bailout
default:
  title="rational julia"
  complex param julparam
    caption="julia parameter"
    default=(0,1)
  endparam
  complex param power
    caption="power"
    default=2
  endparam
  float param bailout
    caption="bailout"
    default=1000
  endparam
switch:
  type="rational-mandelbrot"
  power=power
  bailout=bailout
}

I have opend your formula in wine/UF5 but image is different
?