Fractal Movie --- The Mandelbrot Set

Did you ever have an itch you just had to scratch? This movie was like an itch for me that had to be scratched.

I first learned of the Mandelbrot Set back in the early 1990's. I don't recall the precise year. At the time, I had a 33Mhz 80386 based machine with the 80387 math co-processor available to me. I put it to work calculating some pretty images. I never got very far though. Any decent zoom requires a lot of floating point operations to produce a good image. Still, that didn't stop me from doing some cool stuff which is now lost.

Making a movie back then for me was out of the question. Today that is not the case. I have a more powerful computer at my disposal. It is no supercomputer, but it is much faster than that old 386. It is a dual Athlon 1800+ MP with a gigabyte of RAM to work with. My thoughts had recently turned back to my old friend The Mandelbrot Set. Not only did I have the Athlon box (running Debian Linux) to play with, but I also have an Apple Powerbook G4. That spells movie.

The Movie

FZ1_1.png

This is what an uncompressed frame from my rendering of the Mandelbrot Set looks like. I caclulated 1801 frames for my movie. I then imported the individual frames into QuickTime 6.5. Each frame was generated at 480x360 resolution and each pixel got one of 1501 colors assigned to it.

Here are some statistics on the uncompressed movie:

  • Data Size: 890.7 MB
  • Data Rate: 14.8MB/sec
  • Duration: 00:01:00.02
Fractal-Zoom-1v5.mov

Sadly, to make it feasible for me to share my production, the movie has to be compressed. I used iMovie to suck in the movie clip I had created with QuickTime. While I was there, I added some opening titles and an audio track from Wagner that happened to very closely match the length of the animation. If that isn't an artistic selection, then I don't know what is.

After I finished mucking about with the movie in iMovie, I exported it back out as a QuickTime movie using the MPEG-4 codec for both video and audio. Here are some stats:

  • Data Size: 34.4 MB
  • Data Rate: 376.8 K bytes/sec
  • Duration: 00:01:33:13
Fractal-Zoom-1v1.mp4

I also exported a version in mp4 (MPEG-4) format for playback on less capable machines or by people without QuickTime 6 (I hope). The mp4 file is also knocked down to 320x240 pixels. Bleh.

Here are some stats for the mp4 file:

  • Data Size: 10.3 MB
  • Data Rate: 112.9 K bytes/sec
  • Normal Size: 320x240 pixels
Fractal-Zoom-1v0-sa.mp4

Even the smallest files can be cut down in size some. I decided to include a version with no opening titles or audio. It should play on all MPEG-4 players. Perhaps even phones.

Here are some stats for the little mp4 file:

  • Movie FPS: 14.99
  • Data Size: 460.1 K
  • Data Rate: 7.6 K bytes/sec
  • Normal size: 160 x 120 pixels

The last three images are also links to the files they represent. Click on one of them or whatever to download the file.

The individual frames are now available in TIFF format here.

If you don't have QuickTime, you can get it from Apple for Windows or Macintosh here.