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I open a new topic for this, but I think this theme is related to coupled systems (http://www.fractalforums.com/mandelbrot-and-julia-set/coupled-mandelbrot-sets-%28cms%29/ (http://www.fractalforums.com/mandelbrot-and-julia-set/coupled-mandelbrot-sets-%28cms%29/)), because of the similarity of patterns.

The idea is: add random noise to every variables after each iteration. You have to use the same series of random numbers for each pixel to get a coherent image.



Noisy Mandelbrot (not coupled, just one single set):

Img #1: the neck (top) of period-3 bulb: random wormholes (Ampl=1E-3)
(http://s33.postimg.org/kbpehzbgv/fra_kep0001.png)

Img #2: a zoom of Img #1: empty patterns. Only the size of patterns is fractal-like, but the figures are filled with a single color, not with patterns (as we saw at coupled systems) (Ampl=1E-3)
(http://s33.postimg.org/flwapamdr/fra_kep0002.png)

Zoom series #1: (Ampl=1E-3)
(http://s33.postimg.org/dq1h51j67/mandelbrot_0001.png)

secoundary pattern lane, and non-smooth surface:
(http://s33.postimg.org/rnxffkle7/mandelbrot_0002.png)

(http://s33.postimg.org/mf6zvfscv/mandelbrot_0003.png)

(http://s33.postimg.org/ftccw2zwv/mandelbrot_0004.png)


Zoom series #2: (Ampl=1E-3)
(http://s33.postimg.org/kfhnvx07j/mandelbrot_0005.png)

(http://s33.postimg.org/rileh5x73/mandelbrot_0006.png)

wormholes
(http://s33.postimg.org/4a8qpcuvj/mandelbrot_0008.png)

empty patterns
(http://s33.postimg.org/t4sp2swnj/mandelbrot_0009.png)

(http://s33.postimg.org/g7sun12z3/mandelbrot_0010.png)


Zoom series #3: (Ampl=1E-3)
(http://s33.postimg.org/mquvrftxr/mandelbrot_0011.png)

disappeared black area
(http://s33.postimg.org/96mzi713j/mandelbrot_0012.png)

(http://s33.postimg.org/wq7wva53j/mandelbrot_0013.png)

(http://s33.postimg.org/h9yxyqpu7/mandelbrot_0014.png)

(http://s33.postimg.org/9y79yfbrj/mandelbrot_0015.png)

(http://s33.postimg.org/g71sjho3z/mandelbrot_0016.png)

(http://s33.postimg.org/u6856t93j/mandelbrot_0017.png)

There are no nondivergent areas here
(http://s33.postimg.org/m3j5mz39r/mandelbrot_0018.png)

Zoom series #4: (Ampl=1E-3)
Burning ship, inner coloring (http://www.fractalforums.com/new-theories-and-research/a-new-look-into-escapetime-fractals-using-abs-and-inner-coloring/msg53013/#msg53013)
(http://s32.postimg.org/f3c5lxz9h/burning_ship_0001.png)

(http://s32.postimg.org/6ix2jda6d/burning_ship_0002.png)

(http://s32.postimg.org/po9ikm3lx/burning_ship_0003.png)

You have to increase the iteration number to get a more detailed image
(http://s32.postimg.org/6v636kyx1/burning_ship_0004.png)

Empty areas between the pillars (normally not common inside the miniships)
(http://s32.postimg.org/sjdx6wm9x/burning_ship_0006.png)

Overlapping periodic point and fractal pillars
(http://s32.postimg.org/5xmdzecp1/burning_ship_0007.png)

ImageX
(http://s32.postimg.org/l0cefb1dx/burning_ship_0008.png)

The fractal patterns continue
(http://s32.postimg.org/fuafvr1dx/burning_ship_0009.png)

Get noisy: overlapping random patterns and periodic points
(http://s32.postimg.org/ihddsrsg5/burning_ship_0010.png)

There are still fractal patterns; zoom: 3E10 times
(http://s32.postimg.org/jml83dj2d/burning_ship_0011.png)

But if you zoom into a different area of imageX...
(http://s32.postimg.org/scrhvpfb9/burning_ship_0008a.png)

...empty patterns found (really empty: no patterns even at very large iteration numbers)
(http://s32.postimg.org/l2a886k05/burning_ship_0009a.png)

this is sooo cool!
I love it how the mandelbrot set becomes even more alive and "more realistic" through this! :)
these are awesome:
(http://s33.postimg.org/rileh5x73/mandelbrot_0006.png)
(http://s33.postimg.org/4a8qpcuvj/mandelbrot_0008.png)

cheers!
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Here is an article from the scientific side of the world (requires access to ScienceDirect):
Research on characteristics of noise-perturbed M–J sets based on equipotential point algorithm, 2016:
http://www.sciencedirect.com/science/article/pii/S1007570415002221 (http://www.sciencedirect.com/science/article/pii/S1007570415002221)

I think fig. 3.a)-c) shows the evolution of the empty patterns: as the added noise increases, the fractal becames disconnected and a part of it slowly escapes.

Some free articles:

Role of Superior Iterates in Optimizing the Dynamic Noise, 2013
http://research.ijcaonline.org/volume64/number20/pxc3885618.pdf (http://research.ijcaonline.org/volume64/number20/pxc3885618.pdf)

The Generalized Julia Set Perturbed by Composing Additive and Multiplicative Noises, 2009
http://www.emis.de/journals/HOA/DDNS/Volume2009/781976.pdf (http://www.emis.de/journals/HOA/DDNS/Volume2009/781976.pdf)

the question is:

CAN YOU ANIMATE THIS ?

Sure. I plan to make animation about increse the noise amplitude, but before that I play a little bit more with it.

Mandelbrot with tentacles, so to speak... I don't know, I prefer the original.

Although some of the pictures in Zoom series #4 are quite aesthetic too.

An animation is made of Img #1, with increasing amplitude of noise from 1E-4 to 5E-2 (on log. allocation).
Video #1:
https://youtu.be/F7Wm7IFYQGY (https://youtu.be/F7Wm7IFYQGY)

that video is what happens when you take a hit of dmt and then look at the standard mandelbrot  :o

 88)
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Img #3: a Julia set of Mandelbrot + noise system
(http://s33.postimg.org/lce4fakdb/Julia_proba.png)