January 26, 2010

Mandelbrot Ultra Zoom #5: 2.1E275



Description
The final magnification is 2.1x10^275 (or 2^915). I believe that this is the deepest zoom animation of the Mandelbrot set produced to date (January 2010).

Each frame was individually rendered at 640x480 resolution and strung together at 30 frames per second. No frame interpolation was used. All images were lovingly rendered by 12 CPU cores running 24/7 for 6 months.

Music
"Research Lab" by Dark Flow.

Coordinates
Mandelbrot
Final zoom location:
real=-1.7400623825
7933990522
0844167065
8256382966
4172043617
1866879862
4184611829
1964415305
6054840718
3394832257
4345000825
9172138785
4929836778
9336650341
7299549623
7388383033
4646546129
0768441055
4861368707
1985055926
9507357211
7902436669
4013479375
3068611574
7459438207
1288525822
2629105433
6486959460
03865

img=0.0281753397
7921104899
2411521144
3195096875
3907674299
0608570401
3095958801
7432409201
8638540081
4658560553
6156950844
8677407700
0669037710
1916653380
6041899932
4320867147
0287689837
0483131652
7873719459
2645920846
0043315033
3362859318
1020170329
5807479996
6721030307
0821501719
9479847808
9798638258
639934

magn=2.0667172E275
max iterations=10,000,000

Download WMV (640x480 medium quality - 86MB)
Download MP4 (640x480 medium quality - 234MB)
Download WMV (640x480 full quality - 539MB)

20 comments:

deepskyfrontier said...

2.1E275. Something like seven universes? Where an individual particle becomes the size of a universe, and then an individual particle is chosen from withing that universe- and so on- a total of approximately seven times? It's an amazing work of exploration. It's breathtaking. And you can continue it, can't you? Go deeper?

deepskyfrontier said...

Here's how I explained it on my Facebook page: "If you were to start with the whole universe in front of you, and then zoom in on a single particle (an electron for instance)- and that particle then became a universe, and you were to zoom in on a single particle within that universe, and then that particle were to become a universe, and you were to zoom in on a single particle within that universe, and then that particle became a universe, and you were to zoom in on a single particle within that universe, and then that particle became a universe, and then you were to zoom in on a single particle within that universe, and that particle became a universe, and then you were to zoom in on a single particle within that universe, and at that point you found yourself essentially back where you started, that's the zoom-scale equivalent of what you'll find in this video of the Mandelbrot Set, which can be described, in mathematical notation, with less than 30 symbols. Even if Moore's Law continued unabated for trillions of millenia, and all the mass in the universe were turned into data storage to simply contain the specific coordinates of ever-deeper points of exploration, the Mandelbrot Set still could not be fully explored. You could say that it's more complex than the universe... if not for the fact that the universe has the Mandelbrot Set in it."

pascal said...
This comment has been removed by the author.
pascal said...

Which software did you use? (I can see how it would take that long, since the precision is way beyond ordinary floating point numbers, but how does one implement that, actually? Or is there an Integer-Mandelbrot formula?)

Orson said...

Check out this excellent summary of existing fractal programs. The key phrase to use on search engines is "arbitrary precision".

https://www.fractalus.com/fractal-art-faq/faq06.html

felix said...

Was the coordinate you zoomed to specifically chosen to give interesting patterns the whole way down, or would any point do that? I ask because there are less complex areas to the side of the zoom center that look like they would show a uniform flat color forever. On the other hand I find it hard to imagine that you could have manually discovered a special coord that deep down that works at all levels of zoom.

Orson Wang said...

@felix The point was chosen to be interesting. I explored other locations that I found to be less interesting or too computationally intensive. After one spends some time exploring the Mandelbrot set, one starts getting a feel of where to go to find interesting points. Google "quickman" - an easy, fast Mandelbrot explorer - and see for yourself.

Ken said...

Not a scientist. Not a mathematician.

I understand the basic concepts of which you speak.

But I primarily enjoy this work from an artistic perspective.

The fusion of the ultra zoom data with the Dark Flow track makes for an engaging journey.

Be sure to let Dark Flow know that I bought their CD on Amazon after hearing several of their tracks in your videos.

All the best and keep up the good work!

- Ken

Orson Wang said...

@Ken - I'm glad you enjoyed the fractal video and the music (I'll pass along the word). BTW, the album cover for Dark Flow's album is actually a color-modified version of this picture: http://fractaljourney.blogspot.com/2007/09/sunset-mirror.html

If you get the physical CD, the disc actually uses this image: http://fractaljourney.blogspot.com/2007/05/saturday-confetti.html

Dark Flow is also a Mandelbrot fan!

Alan Harriss said...

I love this video and would like to download the full quality file , but the link is dead. Is there any way to download?

Alan Harriss said...
This comment has been removed by the author.
Orson Wang said...

@Alan Harriss Thanks for spotting the dead link. I have uploaded to a new host and updated the link.

Juan Orlandini said...

It seems like the video link is dead again. Is there any way you can upload it again?

Thanks!

Orson Wang said...

I found a better file host. I hope this one sticks! Thanks for your patience.

Pascal said...

this is absolutely awesome...
I just finished my own program to make Mandelbrot zoom videos, but will never have the time and specs to do such an amazingly deep zoom!
But I used your coordinates so that i have a good starting point.
How do you find coordinates that work?

Orson Wang said...

Finding the coordinates took almost as much time as rendering the zoom. Finding the coordinate is mostly trial and error. After some practice, though, most people will learn to zoom in on vanishing points for areas of interest and self similarity.

Anonymous said...

The video looks great, but it uses the absolutely most annoying download system I have seen in 20 years of the Internet.

Anonymous said...

Would I be possible to share further details about the software/hardware configuration used for this creation ? For instance, the description states that "All images were lovingly rendered by 12 CPU cores running 24/7 for 6 months.". You mean, 12 GPU, right ? Otherwise, do we talk about 12 dies or 6 CPU + Hyperthreading ? Did you use a rendering computer or an ordinary workstation ? I'm really curious about the hardware behind this marvel :)

Thank you

Orson Wang said...

I used three computers with quad-core processors, such as Intel Q6600. Software was Ultra Fractal, which scales perfectly with processor cores.

Irving Dallas said...

Awesome images!

For those interested in programming, here's a tutorial on Mandelbrot in just 25 lines of JavaScript:

http://slicker.me/fractals/fractals.htm