For technical explanations (equations and parameters), see : MANDEL01 fractal.
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Parameters used here (on a particular area of MANDEL01 fractal) :
real perturbation : 0, imaginary perturbation : 0
bailout test : mod, bailout value : 4

Note : all the fractals of this series of images are various areas of fractal MANDEL01
with zooms reaching sometimes very high values.

Here we have for MANDEL11XA :
Magnification : 705,200,000,000,000,000 (or 7.052 x 10 ^ 17) / Calculation time = 14 hours 36 minutes 21 seconds.

New zoom on the center of image MANDELXA.
Name of the image : MANDEL11XAA
Magnification : 984,800,000,000,000,000 (or 9.848 x 10 ^ 17) / Calculation time = 15 hours 28 minutes 48 seconds.



New zoom on an area of the above image MANDELXAA (easy to find).
Name of the image : MANDEL11XAB
Magnification : 3,265,000,000,000,000,000 (or 3.265 x 10 ^ 18) / Calculation time = 18 hours 34 minutes 14 seconds.



New zoom on an area of the above image MANDELXAB (easy to find).
Name of the image : MANDEL11XAC
Magnification : 24,000,000,000,000,000,000 (or 2.4 x 10 ^ 19) / Calculation time = 28 hours 24 minutes 00 second.



Image MANDELXAC with another palette of colors.
Name of the image : MANDEL11XAD



With a much larger area, and with the parameter Outside Color = atan instead of iter the fractal becomes as shown below.
Name of the image : MANDEL11XAE
Magnification : 1.659 x 10^4 / Calculation time : 10 seconds.



Information.

1) All the above fractals have been calcukated with an Intel 2.55 GHz processor and a large amount of memory.

2) When the magnification is greater than 10^16, the standard calculation
with the processor and the associated co-processor is not used.
Another complex method of calculation is used,
allowing calculations with a very high number of decimals (the limit is unkown).
But the calculation time increases very quickly with the magnification :
with a magnification of 10^19, the full calculation time reaches more than 1 day (with the 2.55 GHz processor used here).

3) All the fractals MANDELxx of this gallery (included the additional images) are zooms
of various areas located inside the small cyan square (added manually) shown on the image below.
Name of the image : MANDEL00
Magnification : about 1.



Same image without the small cyan square.
Name of the image : MANDELXAF
Magnification : about 1 / Calculation time : 2.9 seconds.



Same image with another palette of colors.
Name of the image : MANDELXAG
Magnification : about 1 / Calculation time : 2.9 seconds.



================================== Information ==================================
Comparison of fractal MANDEL11XAC above (magnification : 2,4 x 10^19) and fractal MANDELXAF (magnification : 1).

In order to compare the sizes of these 2 fractals, we use here the size of the full Solar System.

We start first with a few definitions of the Solar System.
1) One astronomical unit (AU) is equal roughly to the distance from Earth to the Sun : about 150 million kilometers or 1.5 x 10^11 meters.
2) The maximum size of the Kuiper belt is around 50 AU (= 7.5 x 10^13 meters).
3) The maximum size of the theoretical Oort cloud is 200.000 AU (= 3 x 10^16 meters).

All these distances mean that fractal MANDEM11XAC, with a magnification of 2.4 10 ^ 19,
if displayed on a 0.5 meter width screen,
represents an area located far away the Oost belt compared with fractal MANDEL00 (or fractal MANDELXAF).
This area would be 1,600 times furher the maximum size of the Oost cloud.
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The two images below are not fractals.
Spherical projections of fractal MANDEL11XAF have been made, and then the results have been overlaid on the fractal.
This processus is generated with the FRACTINT commands.
Name of the image : MANDELXAH



Name of the image : MANDELXAI