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Author Topic: Guide to the Inner Workings of the Mandelbrot-Set 1  (Read 5481 times)
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Chillheimer
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« on: October 11, 2014, 12:44:11 AM »

During the last years and countless zooms with Kalles Fraktaler I slowly started to get a grip of the inner workings of the M-Set.
I don't know if most of you are already aware of this, and to most people on our (fractal;)) planet this knowledge probably is useless..
But I would have loved to have some kind of guide or map to the M-Set when I started discovering it.

There is the page by miquel, which I highly recommend to newbies:
http://www.miqel.com/fractals_math_patterns/mandelbrot_fractal_guide.html

But I was searching for some info about different yet similar zoom paths and how a small decision in the beginning does affect the later outcome.
so here we go:
1, left side shows the main bulb
2 right side shows the same area but on the 2nd circle.
this lengthens the end of every(!) branch by 1 extrabranch, with 2 sub-branches on each side. hard to explain, just take a close look:

dl this for higher resolution: http://www.chillheimer.de/Fraktal/content/Parallel_combo.jpg


3d is cool.. but the surface of the 2d-mset still seems to be relatively uncharted territory. lets change this!


Please respond if you find this helpful and I will upload other, more complex examples..

update may2015:
timothychase did an awesome morphing video that does what I try to describe here in an incredible videosequence:

<a href="http://www.youtube.com/v/TzE-XDebDog&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/TzE-XDebDog&rel=1&fs=1&hd=1</a>
« Last Edit: June 09, 2015, 10:11:53 PM by Chillheimer » Logged

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Kalles Fraktaler
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« Reply #1 on: October 11, 2014, 11:50:46 AM »

Nice, please show a more complex example  smiley
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Chillheimer
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« Reply #2 on: October 14, 2014, 01:21:25 PM »

Okay, one more..

dl this for higher resolution: http://www.chillheimer.de/Fraktal/content/branch_compilation.jpg



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cKleinhuis
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« Reply #3 on: October 14, 2014, 02:05:25 PM »

nice, would be cool to see an illustration of the "morphing" features as well, e.g. 2 pathes from a starting location explaining how the morphing can be used

how did you map the farther zooms? by hand ?!
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Chillheimer
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« Reply #4 on: October 14, 2014, 02:36:38 PM »

nice, would be cool to see an illustration of the "morphing" features as well,
I don't understand what you mean by "morphing"..
e.g. 2 pathes from a starting location explaining how the morphing can be used
Isn't that exactly what I was doing?
2 different paths, showing how they affect the "same" structure..

how did you map the farther zooms? by hand ?!
you mean colour mapping?
yep. lot's of trial and error.
If there is a way to do this automatically, I'd love to know..
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youhn
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« Reply #5 on: October 14, 2014, 06:40:20 PM »

I don't understand what you mean by "morphing"..Isn't that exactly what I was doing?

Just watch
<a href="https://www.youtube.com/v/iF-eJO28gko&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/iF-eJO28gko&rel=1&fs=1&hd=1</a>
and notice how the shape of the embedded julia changes. This is called julia morphing, or morphing in short. Although I think it's a too general word, because shifting the start point in the real/imag plane is also a kind of morphing. Which is (confusingly) called perturbation sometimes ....

Naming stuff brings pain, sometimes pictures or videos work better.
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youhn
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« Reply #6 on: October 14, 2014, 09:25:34 PM »

Short image tutorial on shape stacking. The paths intertwine! Do compare the end results and how they came to be. For experts, jump to the end and find the zoom path that was used down to e57. Good luck everyone.   cheesy



...zoom, zoom, zoom, morph those shapes, decrease color density by 50% ....



I made a small mistake in the order of the series. Should not be hard to find. Question: where should the wrongly placed image be instead?
« Last Edit: October 14, 2014, 09:28:41 PM by youhn, Reason: use mistake as question for other » Logged
cKleinhuis
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« Reply #7 on: October 15, 2014, 12:00:54 AM »

super nice, thank you, this i am going to talk about in the artsy-fartsy part of my youtube show wink the gallery

very nice pictures, the video is aweseom, deep zooming really rocks da house!

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divide and conquer - iterate and rule - chaos is No random!
Chillheimer
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« Reply #8 on: October 18, 2014, 01:38:53 PM »

thx for clarification!
I didn't know that the technique even has its own name.. shapestacking..
It's so much fun to be able to actively shape your results, instead of just zooming in randomly.

Maybe you have the multipicture in a higher resolution?
I'd love to take a closer look..
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youhn
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« Reply #9 on: November 10, 2014, 10:34:51 PM »

 cool
Bump ...

This guy on Deviantart really likes to morph, making frog-like structures. Thought I had to share this:

http://stevi0d.deviantart.com/

Some examples:



and

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cKleinhuis
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« Reply #10 on: November 10, 2014, 10:41:53 PM »

wau wau waz
hehe, i meant
wow wow wow
this is so nice
to see people extending the ideas by using them woah, especially the last one is looking at me wink
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divide and conquer - iterate and rule - chaos is No random!
Chillheimer
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chilli.chillheimer chillheimer
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« Reply #11 on: November 19, 2014, 10:21:36 AM »

I did a short zoom movie that shows how shapestacking works a little better than still pics:

<a href="https://www.youtube.com/v/JxkNEvcU8cY&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/JxkNEvcU8cY&rel=1&fs=1&hd=1</a>

in the picture below you see the stacked previous path very close to the minibrot.
I find  it fascinating, that even the number of shapes stays the same after each bifurcation. for example, I zoomed past 17 snake-shapes.. still 17 close to the minibrot..


* shapestack_demo_txt_sml.jpg (251.39 KB, 1920x1080 - viewed 714 times.)
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--- Fractals - add some Chaos to your life and put the world in order. ---
youhn
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Shapes only exists in our heads.


« Reply #12 on: November 19, 2014, 05:40:18 PM »

Maybe you have the multipicture in a higher resolution?
I'd love to take a closer look..

A bit delayed, but here : http://www.rijckaert.org/jeroen/fractal/innerworkings.jpg
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youhn
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« Reply #13 on: May 09, 2015, 09:14:58 PM »

Main PC crashed. Bought new MB and CPU, but crashed again. Now on laptop from work, but only M$ Windows and kinda locked down. So since I cannot install a damn thing, I'm only using third party software which runs without installing (the local IT guy at work is flexible ...). Sooooo, back to Kalles Fraktaler instead of Mandelbulber.

Dove into some low-level Julia morphing, trying to get as much variety without zooming very deep. At the moment I really like those "closed" shapes which spirals can make. This gives the illusion of bounded shapes, for example those frog like structures in the post above.



Source: http://jeroensnake.deviantart.com/art/Odd-legged-spiral-square-duck-heads-532013769
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Kalles Fraktaler
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« Reply #14 on: May 10, 2015, 10:10:41 AM »

Looks good!

Have you tried to use "show inflection" to help you decide where to zoom further into a nice location?
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