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The Mandelbrot Set

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gibran2

gibran2

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I noticed a number of users have been using images from the Mandelbrot set as their avatar, so I thought I’d post a few images I just generated. The application I used is called “quickman” and it’s amazingly fast at rendering. Enjoy.
 

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I don't know why anyone would use the mandelbrot set as their avatar - that's just silly:wink: !

JBArk8)

PS - nice work!! I might have to change my avatar!!
 
Aye I'm guilty as charged. Very enjoyable pictures indeed. For the history buffs, I've been told by a mathematician-in-the-know that the Mandelbrot Set actually shouldn't be called the Mandelbrot Set. Mandelbrot didn't know how to use a computer to print out a visual depiction of the set of complex numbers that make up the "Mandelbrot Set". A French mathematician by the name of John Hubbard showed him how to use the primitive computers of the time to plot out the Set as well as a related set (or more accurately set of sets) known as the Julia set (yielding some equally beautiful images), but gave Mandelbrot the credit for the work since he had already begun investigations into the set. The reason the set is so famous is for its visual beauty, so the set should really be known as the Hubbard Set, since Hubbard figured out how to print it out visually! Interestingly the wikipedia article does not give this version of the story which comes from people directly involved.

It appears this and related areas of study in mathematics - dynamical systems, "chaos theory", differential geometry, etc. - both influenced and were influenced by psychedelics; they certainly provide beautiful visualizations for displays at psy-trance and Grateful Dead shows, as well as models for psychedelic experiences, and in turn I think it's not a coincidence that these subject areas flourished after the "psychedelic revolution" of the 60's. Here's a paper from Ralph Abraham on this very subject: http://www.maps.org/news-letters/v18n1/v18n1-MAPS_8-10.pdf. He describes the shift towards thinking of mathematics as the study of space/time patterns and describes the effects his DMT/LSD experiences had on his evolution as a mathematician. Rich stuff.
 
Thanks for post that quickman program is pretty cool! Here is a couple images I captured really easy and quick program.
 

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Since this was about a Mandelbrot Set here is a couple that actually contain that image loving messing with this program.
 

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While great fun these programs are, if you're 'really' serious about fractals, I'd suggest (get 'yer CC out) UltraFractal.
I've been 'into' fractals since 1984 (even attended a seminar at Delft Tech Uni where Benoit lectured once), and this is, IMHO, by far the most sophisticated program out there. Photoshop buffs will love it's layers. Janet Parke (amongst others) works miracles with it.
I cannot post any of my most treasured works because I believe that if it's so good I must print it, I destroy the digital original. And if its not good enough to print, I delete it anyway. Suffice to say, being the perpetual (!) self-critic, I don't have much on my PC of my stuff.

Now that I project back, I once 'discovered' the end of the Mandelbrot-set once... turned out I reached the end of the floating-point capabilities of my trusty CBM64 home-computer.... go figure...

Peace!


PS: guess I spilled the beans on my age with that CBM64 remark..... I admit, I'm a yakyakker.
 
TmC47 said:
While great fun these programs are, if you're 'really' serious about fractals, I'd suggest (get 'yer CC out) UltraFractal.
I've been 'into' fractals since 1984 (even attended a seminar at Delft Tech Uni where Benoit lectured once), and this is, IMHO, by far the most sophisticated program out there. Photoshop buffs will love it's layers. Janet Parke (amongst others) works miracles with it.
Click to expand...
Thanks for the link. I really like the unlimited digit precision. (quickman is limited to the CPU floating point max). I’m tempted to buy the application, but it’s hard to justify the price.
Hmm…

Also, here’s a link to a recent TED Talk by Benoit Mandelbrot.

benzyme said:
some of those look more like Julia sets (which are prettier, imo)
Click to expand...
All of my images are Mandelbrot, and I think all of the others are as well. Goes to show how varied the set can be.
 

"For each point in the M-Set there is a corresponding Julia-set,
the difference is J-sets repeat themselves perfectly over and over as you "zoom in"
by Iterating the equation into finer and finer points on the grid.
The M-set however changes constantly as you zoom in, and is a single continuous line that maps the transition
between Every possible julia set (from a straight line to a million-coil spiral to lightning like fragments)."
 
Evening Glory said:
Ah, I love fractals!! For some of the best Mandelbrot porn out there, visit Mandelbulb. The images feel exceptionally familiar! 8)
Click to expand...
Someone posted this link a while back, but I had forgotten about it (the link, not the incredible images). Thanks for posting it!

Some of those images are eerily similar to what I see when I break through. You too?
 
imPsimon said:
Incredible 3d fractal
vimeo.com

The Formula

Music: www.wearetheformula.com Video: www.subblue.com www.hohumrecords.com
vimeo.com vimeo.com

and a very nice zoom from teamfresh
vimeo.com

Last Lights On - Mandelbrot fractal zoom to 6.066 e228 (2^760)

download the 1.8GB mp4 @ http://www.hd-fractals.com/downloads/ What can I say? how about the bare facts. I will let you make up your mind about the animation itself…
vimeo.com vimeo.com
Click to expand...
That zoom is incredible!

This one reminds me very much of the breakthrough “membrane”:

Mandelbulb zoom


edit: That teamfresh zoom video also gives one a sense of just how big infinity really is. Imagine zooming in, not for 14 minutes, but for billions of years. And after those billions of years, there would still be infinitely more detail to zoom into! Mind-boggling…
 
benzyme said:

"For each point in the M-Set there is a corresponding Julia-set,
the difference is J-sets repeat themselves perfectly over and over as you "zoom in"
by Iterating the equation into finer and finer points on the grid.
The M-set however changes constantly as you zoom in, and is a single continuous line that maps the transition
between Every possible julia set (from a straight line to a million-coil spiral to lightning like fragments)."
Click to expand...


Excellent primer for all those interested!
Thank you!
 
I've used Ultrafractal quite a bit, and agree that it's the best by far.

Here's one of mine.

nice.jpg
 
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