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Author Topic: Buddhabrot fractals  (Read 9017 times)
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Buddhi
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« on: July 25, 2009, 07:22:51 PM »

Some time ago I played with Buddhabrot fractals. If you don't know what is Buddhabrot fractal, look at http://en.wikipedia.org/wiki/Buddhabrot

To render Buddhabrot in very high quality I had to use very accurate grid of resolution: 50000 x 50000 samples and calculate fractal in very high number of iterations - 50000 !!!. It takes about 35 hours to render this using Intel Core 2 Quad Q8200  the wave



Try to watch in high quality (double click on video)
<a href="http://www.youtube.com/v/QsWEbx2wOBM&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/QsWEbx2wOBM&rel=1&fs=1&hd=1</a>

And some detailed view:

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Pauldelbrot
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pderbyshire2
« Reply #1 on: July 26, 2009, 06:03:44 AM »

The last image reminds of NASA Hubble images of nebulae in deep space.
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Timeroot
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« Reply #2 on: March 07, 2010, 07:45:54 PM »

Maybe the clearest way to communicate with extraterrestrial life would be trying to re-shape some gas into a gigantic buddhabrot...

(Note I said "clearest", not "easiest")  wink Nice pics!
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
kram1032
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« Reply #3 on: March 07, 2010, 08:29:39 PM »

lol.
Why not use a Buddhagram? xD
Or, to create a 3D-variant: Somewhere I found a WIP-Buddhabulb on one of the pages, of one of the forum members... (Was it David Makin, maybe?)
I'd love to see that explored further smiley
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David Makin
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« Reply #4 on: March 07, 2010, 08:50:24 PM »

lol.
Why not use a Buddhagram? xD
Or, to create a 3D-variant: Somewhere I found a WIP-Buddhabulb on one of the pages, of one of the forum members... (Was it David Makin, maybe?)
I'd love to see that explored further smiley

I think I remember somesuch...but it wasn't me smiley
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FractalWoman
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« Reply #5 on: April 21, 2010, 10:13:19 PM »

Hey everyone. I just joined this blog and was very excited to see some Buddhabrot fans. I am FractalWoman (Lori Gardi in reality). I am given credit on Wikipedia for coining the term Buddhabrot, in the Discovery section. I am a computer scientist and Fractal Cosmologist. I have developed a fairly extensive cosmology based on the Mandelbrot Set (and Buddhabrot Set) that can be found here:

http://www.butterflyeffect.ca/Close/Pages/Buddhabrot.html

I hope you have a chance to check it out. I may start a thread on Fractal Cosmology sometime in the future. Could be fun.

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Nahee_Enterprises
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« Reply #6 on: April 21, 2010, 10:22:40 PM »

Hey everyone.  I just joined this blog and was very excited to see some Buddhabrot fans.
I am FractalWoman (Lori Gardi in reality).  ......
I may start a thread on Fractal Cosmology sometime in the future.

Greetings, and Welcome to this particular Forum !!!    smiley

There are a few fans of the Buddhabrot here, though it seems the Mandelbulb/box area is the most current trend at the moment.  But who knows how long that will last.  Something totally new may come along to replace it.    wink
 
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cKleinhuis
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« Reply #7 on: April 21, 2010, 10:57:08 PM »

@fractalwomen, i knew it you where the founder of the buddhabrot, great to have you abroad, and i hope you have discovered the philosophy section!
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divide and conquer - iterate and rule - chaos is No random!
FractalWoman
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« Reply #8 on: April 22, 2010, 03:46:18 AM »

Cool, Thanks.

This is already way more fun than the science forum I was on earlier this year. They were pretty harsh to say the least. I will definitely check out the philosophy section. Looking forward to many interesting discussions...

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FractalWoman
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« Reply #9 on: April 22, 2010, 05:12:02 AM »

I was wondering if anyone else uses the following method for speeding up buddhabrot calculations. I was able to speed mine up by an order of magnitude. What I do is I take advantage of the limited number of bits available to the CPU for processing. For each iteration, you check to see of either the real component or the imaginary component is exactly the same as the last iteration. some pseudo code below.

double real;
double imag;


while ! done

iterate();

if (oldReal == real || oldImag == imag)
   Point is on inside. Stop.
else
   oldReal = real;
   oldImag = imag;

repeat


Yes, I know that comparing floats directly is not a good idea, but in this case it is.

Anyways, since buddhabrots are histograms of the "outside" points, then detecting the inside points quickly is really useful.

FractalWoman

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aluminumstudios
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« Reply #10 on: April 22, 2010, 06:28:37 AM »

Hi.  Very nice renderings. 

You might be interested in seeing my entry into the Fractal Forums contest smileyhttp://www.fractalforums.com/index.php?action=gallery;sa=view;id=2048

Regards,

Will Milberry
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Pauldelbrot
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pderbyshire2
« Reply #11 on: April 22, 2010, 07:49:28 AM »

Brent's algorithm for periodicity detection works wonders for speeding up Mandelbrots of every stripe. I never leave home without it. smiley
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FractalWoman
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« Reply #12 on: April 22, 2010, 02:15:12 PM »

Yes, the periodicity method works great but it a bit more CPU intensive than just a quick float compare. It does the trick though.
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Pauldelbrot
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pderbyshire2
« Reply #13 on: April 22, 2010, 11:20:31 PM »

The advantage, besides perhaps earlier detection, is that you can find out the period. The next pixel is very likely to have the same period so a further speedup can be had by testing for that particular period.
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reesej2
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« Reply #14 on: April 22, 2010, 11:28:27 PM »

That periodicity detection method only excludes the period 1 points, right? Admittedly, that's an enormous chunk. Pauldelbrot, you mentioned "Brent's algorithm"? I've never heard the term, any pointers on where I could find that info?

Also, very nice Buddhabrot pics! I like the detail. I find the Metropolis-Hastings algorithm is useful for speeding up things like the Buddhabrot, you don't have to calculate a full grid, but kind of cranky if you try to multithread tongue stuck out That's one of my current projects.
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