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Some images of "Z orbits" of Mandelbrot set iterations Z=Zē+C

These images show the "traces", or "orbits", of the value of the complex number Z during the Mandelbrot-set iteration Z->Zē+C.
A total number of 1 million random C starting points was chosen by the program, each one processed up to 1 million times
using the above formula. Only those Z orbits were drawn onto the canvas which finally diverged, i.e. which escaped to infinity.
A full image at the beginning of each series shows a combination of all orbits, followed by some application screenshots and
finally the smaller images showing only the Z orbits (or Z traces). Each full image will look different due to the random numbers.

If much more than 1 million random C points (e.g. 100 million) are used, and the number of iteratins is much less than 1 million
(e.g. 1000), then the resulting image will be much "smoother" and won't show as many big ring-shaped "objects", because less
iterations will result in less Z values and thus shorter Z orbits. They also look alike since through the higher number of random
starting points the image will show a statistical distribution of all Z values. Some examples of such images, which are often
referred to as "Buddhabrot" due to their similarity to a sitting Buddha if rotated 90° clockwise, can be seen here.

The JavaScript application used to create these images can be found here.
Big numbers of iterations and points can take a while (minutes to hours) – so be patient...


– Series 7 –

Min. iterations: 0, Max. iterations: 1000, Random points: 1 billion


Application screenshot


– Series 6 –

Min. iterations: 1000, Max. iterations: 1 million, Random points: 10 million


Application screenshot


– Series 5 –

Min. iterations: 100, Max. iterations: 1 million, Random points: 1 million


Full image (original, unprocessed)


Application screenshots (click to enlarge)


All logged C points selected: Corresponding Z orbits are shown


Only C point No. 403 is selected


Some single orbits


The next 3 images show the 3 biggest orbits: C675 (818881 iterations), C138 (763521 iterations) and C403 (304140 iterations). They can be easily recognized in the full image above.


– Series 4 –

Min. iterations: 100, Max. iterations: 1 million, Random points: 1 million


Full image (enhanced histogram)


Application screenshots (click to enlarge)


Nothing selected: All Z orbits are shown


Some single orbits


– Series 3 –

Min. iterations: 100, Max. iterations: 1 million, Random points: 1 million


Full image (enhanced histogram)


Application screenshots (click to enlarge)


Nothing selected: All Z orbits are shown


Only one Z orbit selected in list


A few big Z orbits selected (list sorted by iterations, sort order descending)


Some single orbits


– Series 2 –

Min. iterations: 0, Max. iterations: 1 million, Random points: 1 million


Full image (enhanced histogram)


Application screenshots (click to enlarge)


Nothing selected: All Z orbits are shown


All logged C points selected: Corresponding Z orbits are shown


Only a few logged C points selected


A few big Z orbits selected (list sorted by iterations, sort order descending)


Some single orbits


– Series 1 –

Min. iterations: 100, Max. iterations: 1 million, Random points: 1 million


Full image (enhanced histogram)


Some single orbits