An almost high-quality fractal generated with WolframMathematica 10.0
The fractal is made with the formula:
"Im[Nest[Log[Log[#]^(1/#)] &, x + y I, 6]]]"
Where "Im" is the imaginary part, "Nest" is the function for iterate formulas  and "Log" is the natural logarithm written in Mathematica.
Inside the "Nest" function part "Log[Log[#]^(1/#)]", "#" is the place of iterations, and it's iterated 6 times, until end in "x+y I".

This fractal is generated evaluating the following cells:

Formula = 
  Compile[{{z, _Complex}}, 
   Block[{x = Re[z], y = Im[z]}, 
    Im[Nest[Log[Log[#]^(1/#)] &, x + y I, 6]]], 
   RuntimeAttributes -> Listable, Parallelization -> True];

Fractal = 
 Formula[Table[
   x + y I, {x, -3 \[Pi], 3 \[Pi], (6 \[Pi])/(
    3 Round[128 (3 \[Pi])])}, {y, 3 \[Pi], 6 \[Pi], (6 \[Pi])/(
    3 Round[128 (3 \[Pi])])}]]

SystemOpen[
  Export["Fractal (-3pi, 3pi).png", 
   ArrayPlot[Fractal, ColorFunction -> "RedBlueTones", 
    PixelConstrained -> 1]]] // Timing

Where "Timing" is the function to know how much time it took.
Once the last cell is evaluated an image will be saved on "...\My Documents" folder by default and it will be open.
The cells are evaluated one by one in the same ordr than mentioned here, where in this particular case the fractal is shown with the classical "X" & "Y" axis, flipped horizontally and vertically respectively.
In the above example the fractal is defined for an "X" range of -3PI & 3PI, and the "Y" range of -3PI & 3PI.
The different colors of fractal are defined by "RedBlueTones" color function.


**IMPORTANT: If you'll create a fractal like these, it's recommended to restart Mathematica after generating each fractal, because the MathKernel uses many RAM memory (~2GB)**

Here, I'll show a full sample of the fractal with a range of -45PI & 3PI respect of "X", split by 8 parts:

X=(-3PI; 3PI), Y=(-3PI; 3PI)
![](https://d1vof77qrk4l5q.cloudfront.net/img/7e51d99e7da19d5c91fdbc2978c29160617edf8d.png)
X=(-9PI; -3PI), Y=(-3PI; 3PI)
![](https://d1vof77qrk4l5q.cloudfront.net/img/ce3f3ded110a2d1d34dd3ae5d8c3cb2402acddbc.png)
X=(-15PI; -9PI), Y=(-3PI; 3PI)
![](https://d1vof77qrk4l5q.cloudfront.net/img/d58cf3b730ab1a6316835ed68546873a2c65f939.png)
X=(-21PI; -15PI), Y=(-3PI; 3PI)
![](https://d1vof77qrk4l5q.cloudfront.net/img/b7b258dcad3a7f0baac6d6472359dd5fbd6fd835.png)
X=(-27PI; -21PI), Y=(-3PI; 3PI)
![](https://d1vof77qrk4l5q.cloudfront.net/img/3a77a968f9222f50f44ae4cb4ae7fb2a713175a6.png)
X=(-33PI; -27PI), Y=(-3PI; 3PI)
![](https://d1vof77qrk4l5q.cloudfront.net/img/511039e62f771b7407111826b13b02b69bb68c19.png)
X=(-39PI; -33PI), Y=(-3PI; 3PI)
![](https://d1vof77qrk4l5q.cloudfront.net/img/7ca0a5b3dd0595be89677c5eaf23a9d802b05722.png)
X=(-45PI; -39PI), Y=(-3PI; 3PI)
![](https://d1vof77qrk4l5q.cloudfront.net/img/fb14853e0331201781566413e51ebb973b7899c6.png)

Now we'll join all these parts & we reverse colors we'll get something like this:
![](https://d1vof77qrk4l5q.cloudfront.net/img/57d3561677487acdee03c66dfb009cd963328577.jpg)
Hi-res image on "mediafire. com/file/dk1gcnfa4l0ex1s/1A+%28-3pi%2C+3pi%29-.jpg"
This is actually the most giant fractal I've generated by now =D

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