In memory of Benoit Mandelbrot

A tribute to Benoit Mandelbrot (20 November 1924 - 14 October 2010) - a maverick of academia.

Thanks to Dark Flow for the music "Groggy Sunrise".

Planetarium proposal
Ken Hawthorn (at the Fujitsu Planetarium, De-Anza college in Cupertino, California) gave me the idea of projecting a Mandelbrot zoom in a planetarium. Inspired by Dr. Mandelbrot's death last year, I attempted to create a high definition rendering of a Mandelbrot zoom that could be appreciated by those who have never seen it before and could be projected in a Planetarium setting. Synchronization of zoom events against appropriate music is one key element. Planetarium operators are welcome to contact me to use this material gratis via Creative Commons license.

Coordinates
Mandelbrot
Final zoom location:
real=0.0134388705
3201212902
8364919004
0196868675
2857331456
5492885548
699
Img=0.6556142187
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6403994151
735
magn=6.5139268e51
max iterations=10,000,000

Render tech
Each frame was individually rendered at 1080x1080 resolution (1080p) and strung together at 30 frames per second. Sidebands were added for compatibility with standard 1920x1080 resolution. No frame interpolation was used. All images were lovingly rendered by 12 CPU cores running 24/7 for 7 months.

Outtake: Mandelbrot Ultra Zoom #6: 1.0E185

After several abandoned projects (mostly due to render times estimated to be more than 2 years), I finally completed a full zoom.

Description
What is a Mandelbrot zoom blooper? It's what happens when you commit 6 months of computing time on three computers to create something that doesn't turn out the way you expect! The color rotations that begin at 1:36 were unintentional. However, the side effect is that the animation is much more psychedelic than expected due to the color cycling and also brings out details that are not apparent with still images.

Annotations
This animation shows patterns that only a zoom animation reveals - patterns that still images do not convey. For example, note how the "branches" rotate clockwise and counter-clockwise. Furthermore, note how the clockwise rotations double from 2 arms, to 4, to 8, and so on. And note how the counter-clockwise arms also double, although starting from 10. Annotations counting these branches for the first zoom series starts at 0:53.

And if that's not enough detail, consider that when there are 2 branches, the branches rotate counter-clockwise through a 180 degree sweep before evolving into the clockwise (multiple of ten) pattern. When the counter-clockwise patterns return as 4, the branches rotate through a 90 degree sweep before evolving into the clockwise pattern. The set of 8 branches rotate through a 45 degree sweep, and so forth. This type of periodic doubling is common in this region of the Mandelbrot set, but not necessarily elsewhere in the set.

Render tech
Each frame was individually rendered at 720x480 resolution (480p) 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. A YouTube HD version was created by interpolating images to 1280x720 (720p). Although the visual detail is not better, YouTube appears to afford more than proportionately greater bitrates to 720p content, making the video at 720p appear better than at 480p.

Music
"Martian Invasion" by Dark Flow. (Thanks again!)

Coordinates
Mandelbrot
Final zoom location:
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Img=0.6850312970
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magn=1.001113E184
max iterations=1,000,000