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FractalNet

A Mandelbrot fractal generated by FractalNet

Sorry, FractalNet
is not yet available
for public download.
FractalNet is a distributed fractal renderer I wrote, which generates images and videos of the Mandelbrot and Julia sets.  It consists of about 630 lines of C code for fast iteration of the Mandelbrot formula, and about 3,900 lines of Java code for the remainder of the functionality.  Java Native Interface (JNI) is used to connect the C and Java code together.


2010: A Mandelbrot Odyssey

This is my longest and most complicated fractal video so far.  It required 104,066 billion iterations, and took 14 days 13 hours 6 minutes to render.

YouTube fullscreen button Click on this button in
the YouTube player to
watch the video fullscreen.
Watch this video on YouTube  →
Watch this video on Vimeo  →

The video is, of course, inspired by the movie 2001: A Space Odyssey.  For the title sequence, I tried to find a section of the Mandelbrot set which resembles the alignment of the Moon, Earth and Sun in the title sequence of 2001:

The title sequence of 2001: A Space Odyssey (featuring the alignment of the Moon, Earth and Sun), and the title sequence of 2010: A Mandelbrot Odyssey

Click on the image above to see a larger version.


Other videos

Please click on the tabs below to view the available videos.

Video 1 Video 2 Video 3 Video 4 Video 5

A slow deep zoom into the Mandelbrot set.  The original 1920x1080 HD version of this video required a total of 90,459 billion iterations (an average of 26.8 billion iterations per frame).  It took 12 days 1 hour 17 minutes to render on my 2.4GHz iMac.
 
YouTube fullscreen button Click on this button in
the YouTube player to
watch the video fullscreen.
Watch this video on YouTube  →
Watch this video on Vimeo  →

More non-HD videos are available on Vimeo and YouTube.

My HD videos have been included in the HD Fractal Trips group on Vimeo:

HD Fractal Trips

I highly recommend you check out this group, which contains dozens of amazing fractal videos in 1280x720 high-definition.


Images

Please click on the tabs below to view the available images.  Click on a thumbnail to view the full-size image.

Page 1 Page 2 Page 3 Page 4

Creative Commons License These images are licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported License.  You are free to share, copy, distribute and transmit the images, but: you must attribute the images to me; you may not use these images for commercial purposes; you may not alter, transform, or build upon these images.

Lytebox The full-size images are displayed using Lytebox.


Features

Some of FractalNet’s features include:
  • Image output in lossless PNG format.
     
  • HD (high definition) video output in QuickTime format, using QuickTime for Java.
     
  • High levels of anti-aliasing for super-smooth images.
     
  • Smooth gradient colouring (instead of separate regions of uniform colours), using a fully-renormalised fractional iteration count.
     
  • FractalNet's browserA simple “fractal browser” (click here for a screenshot), which allows a user to easily explore the fractals, and view the Julia set corresponding to a particular point in the Mandelbrot set.  Clicking on a point centres the image on that point, and zooms in/out if specified.  Changes in the colour scheme are updated in real-time, without needing to re-render the fractals.
     
  • Generation of videos, using the following techniques:
    • Panning around a fractal.
    • Zooming in/out of a fractal.
    • Rotating a fractal.
    • Colour cycling.
    • Transitioning from one colour scheme to another.
    • Morphing a Julia set, by tracing a path through the Mandelbrot set.
    • A Google Earth style of parabolic flight path between two locations in a fractal – the “camera” zooms out from the initial location, until both the initial and final locations can be seen in the same shot, and then zooms in to the final location.

  • Fast detection of “black areas” (where the iterations never escape to infinity), to speed up rendering by eliminating unnecessary calculations.  See below for more info ↓
     
  • Able to resume rendering a video from a specified frame, if rendering needs to be stopped for some reason.
     
  • Distributed generation of videos, using Java RMI.  A master computer and an unlimited number of slave computers are connected together using a TCP/IP network, and the master uses the slaves to render specific frames of the video.  If the slaves return their frames in the wrong order (ie. because one slave is faster than another), the master rearranges the frames before writing them to the final video.
     
  • Use of a plain text configuration file, which stores all the parameters for an image or video in a user-friendly, human-readable format.

Optimisations 

When rendering a Mandelbrot or Julia set, the most time-consuming parts of the image are the “black areas”.  In these areas, the iterations never escape to infinity, so every pixel must be iterated to the maximum limit.  Therefore, much time can be saved by using an algorithm to detect these areas in advance, so that they can be immediately coloured black, rather than rendering them in the normal way, pixel by pixel.

FractalNet uses a recursive algorithm to split the image up into blocks, and tests each block to see whether it lies inside a “black area”.  In this way, large areas of the image can be quickly coloured black, often saving a lot of rendering time.

Below is an example of FractalNet’s algorithm in action.  Green blocks were detected as “black areas” and coloured black immediately, without having to be rendered.  Red blocks were rendered in the normal way, pixel by pixel.

Optimised rendering of a Mandelbrot image, using recursively smaller blocks



Buddhabrot

I’ve also implemented a simple Buddhabrot renderer in Java, which can either use the simple greyscale algorithm, or a rainbow algorithm by Paul Nylander.

Simple greyscale Buddhabrot with a slight blue tint Rainbow Buddhabrot (shallow iterations) Rainbow Buddhabrot (deep iterations)
Simple greyscale Buddhabrot with a slight blue tint Rainbow Buddhabrot (shallow iterations) Rainbow Buddhabrot (deep iterations)


Referrers

On 16th October 2010, Gawker wrote an article about the death of Benoît Mandelbrot, and they chose two of my fractal videos to illustrate the article (Slow deep Mandelbrot zoom and 2010: A Mandelbrot Odyssey).  Firedoglake embedded one of my fractal videos in a post the following day.

Some articles and blog posts featuring my fractals:
Links

Comments Automatic country lookup for comments powered by MaxMind GeoLite Country

Edd
    11 Jul 2009
    United Kingdom
Wow! If you commercialised this program you'd make a mint!

Email me at epb dot epb dot epb at btinternet dot com (sorry, don't like spam) if you do!
Jim
    26 Oct 2009
    Belgium
So where is the download link?
Michael Hogg
    13 Dec 2009
Sorry Jim, FractalNet is not yet ready for public download.
Brian
    3 Mar 2010
    United States
I just got your comment on youtube. Your newest video is amazing. Will this software eventually be available for windows-based computers? I know that might take a lot more re-coding and programming but it would be great to use this program. I would like to see how long of a zoom I could do, and of course I will give you credit, since you programmed this application yourself. I imagine it took you quite some time. Keep up the good work!
DJT
    3 May 2010
    United Kingdom
Just watched the Odyssey vid and WOW!!! The best Mandelbot animation I've ever seen. Incredibly beautiful and so well put together. Opening sequence caused goosebumps and tear in eye!
Fast zooms are ok but give the impression of flying through rather than zooming in on finer and finer detail like yours do. Thankyou so much for sharing these creations.
Is there any way I can download them to watch in even better quality on a big screen?
Michael Hogg
    8 May 2010
Many thanks for commenting, DJT! Most of my HD fractal videos, including "2010", were rendered at 720p, so I don't have any higher-resolution versions of those available. However, when I get a moment of free time, I'll make some higher-quality (less compressed) versions available for download... watch this space!
sackboy
    17 May 2010
    United States
Hey Michael do you think it's possible to upload a higher quality version of the middle picture in the 2001: A Space Odyssey collage? That movie is my all-time favorite and I absolutely love that revision but the lower quality means it doesn't make for a good desktop wallpaper.
Michael Hogg
    14 Jun 2010
Hi sackboy! Sorry it's taken me so long to reply - I was on holiday! I've uploaded the highest resolution version of the middle 2001 picture here. The fractal is nice and sharp, but I'm afraid the 2001 title is a little blurry (it's taken from the DVD). If you know where I could get an HD (Blu-ray) capture of the 2001 title, then I could make a better quality version!
Daniel
    22 Jun 2010
    Brazil
Please! Make it public! This software must be amazing!!!
hombre
    17 Oct 2010
    United States
a friend was tutored and mentored by mandelbrot, who just died. He is also a musician and was wondering about the music in the slow-deep 12 iteration version?
cheers
Michael Hogg
    17 Oct 2010
Yes, I was sad to hear that Benoit Mandelbrot passed away this week :( How amazing that your friend was taught by the great man himself.

The music in my "Slow deep Mandelbrot zoom" video above is track 1 from Ambessence Piano & Drones by Bruno Sanfilippo & Mathias Grassow. You can buy this album on iTunes here.
Eric Kerner
    1 Nov 2010
    Brazil
i love lsd, the bolota is my life.
Andrew
    6 Nov 2010
    United States
I am incredibly sad to see that he has passed as well. As a math major at university, looking at fractals is definitely an inspiration. I am thankful for his contributions to mathematics as a whole.

As for the fractal generator, is there any plans for making it available for public release? Any thoughts on how much it might cost? (The fractals are awesome, by the way)
Andrew
    6 Nov 2010
    United States
I guess after reading about what distributed computing is, I won't be making stuff like this any time soon! :0 Still, great job.
Michael Hogg
    7 Nov 2010
Thanks for your comments Andrew! If I did ever make FractalNet publicly available, I would probably make it donationware :) But I don't have any plans to release it just yet. There are loads of cool new fractal programs out there - check out the awesome Mandelbulber!
Michael
    22 Jun 2011
    Brazil
Congratulations for the fractals, they are amazing. I am a ecology teatcher in Brazil, and I would using the deep mandelbrot zoom (number 1 - blue) at my classes. The you tube version HD is not perfect. Can you send me a DVD in High resolution? I can pay for the copy and give all the credits about the creation for you.

My mail is rraele@yahoo.com

See you
Ricardo
Nacho
    23 Jul 2011
    Argentina
Michael, your work with fractals is amazing!! I love fractals and was googling HD videos and I came to yours.
The color palette you've chosen is perfect to really relax and enjoy also with genius music.

Thanks for sharing this and keep it up!
kety
    31 Jul 2011
    Israel
I received just today your software - it is really amazing.

I have done some work with other softwares such chaospro and the like.
I also worked with apophyisis, and I enjoyed every moment.

Now I will try to do some work with yours - your work is really amazing, and thanks for sharing!
Chris
    24 Oct 2011
    Greece
Hi! I am writing a fractal software also!
Can I ask how the optimisation works?
I guess you calculate the perimeter and if its all black you paint all the rest of the block black? Can you guide me trough if possible?
Thank you for your time!
Simon Beck
    7 Apr 2012
    France
Hello Michael, Stunning stuff, I was planning on using some of the '2001' music for my own movie, which is still way in the future! I am the snow artist, check out snowartist on facebook! simon
Patrick
    30 Apr 2012
    United States
Hey! I really love your videos!

Could you possibly please email me the program?
I really want to use it!


Keep up the amazing work!

Email:
GinDiamond15@yahoo.com
Elliott
    21 Sep 2012
    United States
Where is the google earth style one?
Maria
    14 Oct 2012
    Finland
Nate, Hey, just saw you won the ti-84 computer...congratulations... My faiorvte approach to the dragon curve is the paper folding approach. I was at a program at the Fermi lab way back in the early 90's and met several of Madelbrot's grad assistants..and several really bright people who were working on bringing fractals and non-linear dynamics to students at a wide range of levels.... and spent some time coming up with methods of generating fractals... oh if we had only had software like this back then.... really nice job, keep up the good work.Pat
xnhoae
    15 Oct 2012
    Canada
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    Netherlands Antilles
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tourist
    12 Nov 2012
    Hong Kong
i dont know if you share your software, because it was definetely quiet an amount of work, but the internet would probably benefit from it. inspired by what i see all the time in my head, i just wrote a program in matlab for the visualization of the mandelbrot-set, but so far i just dont have the mathematical knowledge to optimize the algorithm (5. semester) , so it takes 5 minutes for a picture with 1000000 points... without colours so far, just the shape.
needless to say, i would like to use your program^^ timrebig@web.de
anyway i got some unseen ideas and i will keep up the work. it might take some time... :D
andre1
    27 Nov 2012
    Italy
dear Michael,
is it possible to use your video for make another one with a different music?
thanks byhe
John
    11 Jan 2013
    Netherlands
Hi Machael,
my compliments for your impressive video's, really beautiful and enjoyable. I am curious whether I could get your program software. Fractals are found everywhere around us, in nature, in human body, in universe and in human behaviour. Can you please contact me on following e-mail: thvdwiel@yahoo.com

Thanks for responding and greetings,

Nairolf
    6 Oct 2013
    France
Hey, how about releasing Fractalnet ? Three years have passed now since your last message. It's time to pay attention to people who want to make great use for it :)
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    Poland
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