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Author Topic: Mandelbrot Buds and Branches  (Read 1857 times)
Description: A quick view of the main buds and branches of the cardiod and main disk
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timothychase
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« on: December 25, 2013, 06:29:58 AM »

<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>

Best viewed in 720p HD.

This is the most recent product of an approach I have been developing for the exploration of the Mandelbrot object.  In this case, there are three different types of "quantum zooms" that treat sequences of quasi-regular structures as the basis for frames in an animation so as to visually highlight their similarity and variation.

The central type for this movie consists of sequences of consecutive major buds in a valley, where the image of each bud has been aligned to match up with the others through centering, scaling and rotation.  Another takes the major non-trunk branch of the tree coming off of the bud and uses the branching point and tip for alignment.  A third type aligns the current bud in the same way as the first sequence except that it scales the bud so that the deepest part of the valley remains at a constant apparent distance from the current bud.

Although it is easier to understand the third type once one understands the first, it visually helps to establish the point that one is descending into the valley and that there are a potentially infinite number of buds in the sequence.  So within a triplet of quantum zooms this third zoom actually comes first.

The video has four quantum zoom triplets, one for each of the elephant, sea horse, double spiral and spindle valleys.  Ordinary transitional zooms introduce the first frame in the sequence relative to what came before it by gradually changing the center, scale and angle as needed.  One transitional zoom is from the basic view of the Mandelbrot to the first frame in the first series of the triplet.  Another zooms in from the first frame in the first series to the first frame in the second series of the triplet, then another zooms in from the first frame in the second to the first frame in the third.

I have considered each of the quantum zoom videos to be more or less proof of concept, focusing on relatively shallow regions of the Mandelbrot.  This is no exception, but it is perhaps a little more polished.  The individual frames of each zoom in this video were created separately in Fractal eXtreme, then stitched together into an mp4 using VirtualDub, a free program available at SourceForge.
« Last Edit: December 25, 2013, 11:43:24 AM by timothychase, Reason: missing \"s\" » Logged
eiffie
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« Reply #1 on: December 27, 2013, 06:06:11 PM »

OK I didn't understand any of that but it is really a nice trippy video! smiley haha
You aligned the buds thru scaling etc? You did this with an algorithm I assume? Any hints on how that worked?
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youhn
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« Reply #2 on: January 07, 2014, 11:13:28 PM »

This looks very nice. Reminds me of timelapsed growth.

Did you align by math during the render process, or did you just make lots of images and use some kind of video/image align software ... ?
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cKleinhuis
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« Reply #3 on: January 07, 2014, 11:18:18 PM »

 Smiling Mandelbrot Repeating Zooming Self-Silimilar Thumb Up, by Craig A peacock

gosh, i totally ignored that vid, a fascinating aproach, the growth of the filaments is just awesome!
especially those which exhibit much detail, perhaps re-render with more finer frame rates ? e.g. that one starting at second 45 ?
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cKleinhuis
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« Reply #4 on: January 07, 2014, 11:24:28 PM »

 :hrmm:i see, it is pure handwork, perhaps you can formulate the method in a more technical way so that me might develop some algorithm to create such sequences more or less automatically ?!

so, you just zoom at a point and then align the images by hand ?!  hrmm search  hrmm
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SeryZone
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Contemplate...


« Reply #5 on: June 26, 2014, 02:50:03 AM »

Okay... Just reply...

<a href="http://www.youtube.com/v/zAuHR590m8E&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/zAuHR590m8E&rel=1&fs=1&hd=1</a>
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3dickulus
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« Reply #6 on: June 07, 2015, 10:03:59 PM »

ok, just relpying, poly branches are lovely smiley
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tit_toinou
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« Reply #7 on: June 08, 2015, 02:43:41 PM »

This is awesome !

I've wondered how to compute it in order to automate this kind of videos... Maybe with the formula involving p/q rational bulbs of the mandelbrot set ? (I'm no expert here is a pdf http://matwbn.icm.edu.pl/ksiazki/fm/fm164/fm16413.pdf look at the page 6, or http://en.wikipedia.org/wiki/Mandelbrot_set#Main_cardioid_and_period_bulbs ?)
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Chillheimer
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chilli.chillheimer chillheimer
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« Reply #8 on: June 08, 2015, 09:58:59 PM »

wow!
I didn't see this thread before! awesome work, man! If you achieved this in the way I believe you did, this must have been extremely painstaking work. thank you for sharing!
I added this here: http://www.fractalforums.com/fractal-related-links/inner-workings-of-the-mandelbrot-set-1/ as you did exactly what I tried to show with the still pics..
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