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

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
}