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  Took a trick from my 3+ dimensional formulas, works great with them producing unique beautiful results, and applied it to the classic Mandelbrot set.  Didn't look to great.  Tried the Julia of it, and it looked great. 

  Adds interesting branches to it.

  Calculate z^n, extract your new_x component (prior to adding pixel value to it), and apply the following transform:

  If  (n is 2,6,10,14... etc.)  then {
   if (x>abs(y)) {
      new_x=-new_x;
   }
} else if (n==3 || n==5 || n==7 || n==9) {   
   if (x>0) {
      new_x=-new_x;
   }
}

  Try high Julia seeds.  With real of 0, imaginary of 2/3  (.66666) is one threshold point.  I like around -.142, 1i as well, or around 1.1, very low magnitude i...

  Get some neat stuff- slightly more interesting julias.  See a big difference between a standard julia at 0,1i and this form.

Matt, youforgot images :hit: rofl2

 I so smart....  or lazy.  :D 

  I suppose I should make some images, I just played around a bit.  Pretty quick to render though, so I'll throw a few up... after I've uploaded 'em in a bit.

  Here ye' be.  A link to the album HERE (https://picasaweb.google.com/103496528720991269557/2dJuliasMyType?authuser=0&feat=directlink), and some photos below.  Nothing spectacular, just some Julias.

  Normal 0,1i julia next to switched 0,1i julia:
(https://lh3.googleusercontent.com/-rrDqtPtk-10/T0sAWWQ24ZI/AAAAAAAABTk/8CvJjd07s0Q/s400/Julia%25200%2520%25201%2520%2520normal.jpg)  (https://lh6.googleusercontent.com/-Sq4jMOaKjAI/T0sAWEPOoII/AAAAAAAABTc/5PN3bLHiX6o/s400/Julia%25200%2520%25201%2520%2520with%2520switch.jpg)

1.11, 0  julia switched   julia 1.481  .33 switched
(https://lh5.googleusercontent.com/-XTbsdhjsWko/T0sAWGvR13I/AAAAAAAABTg/P8jPU0vJ8k0/s400/julia%25201p11%25200%2520switched.jpg)  (https://lh5.googleusercontent.com/-ATpaNToZbQg/T0sAWijvQ4I/AAAAAAAABTw/LX0AH75AhUI/s400/julia%25201p481%2520p33%2520switched.jpg) 
julia -1,0 normal and -1,0 switched
(https://lh4.googleusercontent.com/-D77YrIJ_Vpg/T0sAWgI6qFI/AAAAAAAABT0/GCjdeXGfuhk/s400/julia%2520n1p1019%2520%25200%2520%2520normal.jpg)  (https://lh3.googleusercontent.com/-Ho_qXjZtqBw/T0sAWrwBh1I/AAAAAAAABT4/2k95pHDFyMI/s400/julia%2520n1p1019%2520%25200%2520%2520switched.jpg)

then one -1.2 , .3   and two   -1.213,.33  zooms (added the extra -.003, +.03 to sharpen the triangles):
(https://lh4.googleusercontent.com/-4gMhwl0X3XE/T0sAXKI4HII/AAAAAAAABUM/ITjj4sF1YWc/s400/julia%2520n1p2%2520%2520p3%2520%2520switched.jpg) (https://lh3.googleusercontent.com/-dTWX9xSkGWw/T0sAXLKLxoI/AAAAAAAABUI/tk_iGB7Zh28/s400/julia%2520n1p213%2520p33%2520switched.jpg)   (https://lh5.googleusercontent.com/-EwVoY3Y61bk/T0sAXAK5h8I/AAAAAAAABUQ/104pjYLoD2g/s400/julia%2520n1p213%2520p33%2520switched%2520zoomed%2520more.jpg)

  So nothing all that great.  Actually, don't even know if it's anything original- some of them look vaguely familiar.

In fact... Seems a variation/mix of already existing variations :beer:

yeah, just don't recall any specific types.  Are there other Julias that produce those triangle shapes using normal Mandy or BS Mandy formulas?

The functions you used are equivalent to
(x,y) = sort(x,y)
x = -abs(x)

widely used in kifs formulae ;)

 What does the sort(x,y) function do (mathematically speaking)?  Do you have a reference to look at (for me to read)?

  Also, x doesn't always equal -|x| using the rules I posted (so I assume that this has something to do with the sort function). 

  Keep in mind, I'm simply checking (for n=2,6,10...) if x > |y|.  So if x and y are both negative, and y has a greater magnitude, this would return false.