Two Julia-based Formulas for UF by FarDareisMai

It's unfortunate that "Plug-ins" is the best dA category for this, but oh well. The main formula here, "Mated Julias," which you see in the preview images, was actually made by lyc; I just UF-ized it and added a few more variables.

As an alternative to downloading a zip, you can also just copy the following text and save it as a .ufm file:

MatedJulias {
;
; This formula was first implemented in C++ by Thomas Ludwig (lycium), then
; adapted to Ultra Fractal and expanded on by Jess Darling (FarDareisMai).
;
init:
 z = #pixel
loop:
 znum = (z ^ @expnum) + @seed
 zden = (z ^ @expden) - @c1
 m = znum / zden
 n = @seed2 + (@c2 / ((z ^ @coarse) - (@seed2 ^ @fine)))
 z = (m / n) * z
bailout:
 |z| <= @bailout
default:
 title = "Mated Julias"
 param seed
   caption = "seed"
   default = (0.45,0.7794228634)
   hint = "Use this parameter to create many different Julia sets. A good \
           way to set this parameter is with the Eyedropper, or  Explore\
           features."
 endparam
 param seed2
   caption = "secondary seed"
   default = (0.9,0.2931446)
   hint = "This parameter is very sensitive to small changes."
 endparam
 param expnum
   caption = "num exp"
   default = (2,0)
   hint = "This parameter sets the exponent for the Julia formula. \
           Increasing the real part to 3, 4, and so on, will multiply the \
           symmetry of the Julia figure. Non-integer real values and non-zero \
           imaginary values will create distorted Julia fractals. Use (2, 0) \
           for the standard Julia set."
 endparam
 param expden
   caption = "denom exp"
   default = (2,0)
   hint = "This parameter sets the exponent for the Julia formula. \
           Increasing the real part to 3, 4, and so on, will multiply the \
           symmetry of the Julia figure. Non-integer real values and non-zero \
           imaginary values will create distorted Julia fractals. Use (2, 0) \
           for the standard Julia set."
 endparam
 param bailout
   caption = "bailout"
   default = 1024.0
   min = 1.0
   hint = "This parameter defines how soon an orbit bails out while \
           iterating. Larger values give smoother outlines, but may cause \
           the inside portion of the fractal to grow or even fill the whole \
           image."
 endparam
 param fine
   caption = "fine mod"
   default = (2,-0.91667)
 endparam
 param coarse
   caption = "coarse mod"
   default = (2,0)
 endparam
 param c1
   caption = "seed mod"
   default = (1,0)
 endparam
 param c2
   caption = "pos mod"
   default = (1,0)
 endparam
}

SerendipitousJulia {
;
; The result of a mistake made while working on the Mated Julias formula.
;
init:
 z = #pixel
loop:
 znum = (z ^ z) + @seed
 zden = (z ^ z) - @c1
 m = znum / zden
 n = @seed2 + (@c2 / ((z ^ z) - (@seed2 ^ @fine)))
 z = (m / n) * z
bailout:
 |z| <= @bailout
default:
 title = "Serendipitous Julia"
 param seed
   caption = "seed"
   default = (0.45,0.7794228634)
 endparam
 param seed2
   caption = "secondary seed"
   default = (0.9,0.2931446)
 endparam
 param bailout
   caption = "bailout"
   default = 1024.0
   min = 1.0
   hint = "This parameter defines how soon an orbit bails out while \
           iterating. Larger values give smoother outlines, but may cause \
           the inside portion of the fractal to grow or even fill the whole \
           image."
 endparam
 param fine
   caption = "fine mod"
   default = (0,0)
 endparam
 param c1
   caption = "seed mod"
   default = (1,0)
 endparam
 param c2
   caption = "pos mod"
   default = (1,0)
 endparam
}