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
6946506225
1320027664
6174666912
9597586478
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:
real=-0.6367543465
8238997864
3739831915
7140499472
0360213850
2943775952
8815440209
6249756751
3223798252
0103084082
9591065785
2387307099
3324732992
9252845588
8339008633
9317126456
3425878268
8785118895
3461652529
1202
Img=0.6850312970
8367730147
6087839141
7437674213
1010988777
5075070904
9508452703
4567485134
8147467091
9233270255
5722504984
6615654152
7052675399
4100213876
1943853722
2657615602
8819018787
4239788845
0551930772
4466
magn=1.001113E184
max iterations=1,000,000

Benoît Mandelbrot (November 20, 1924 - October 16, 2010)

Thanks to Geri Sullivan and the internet, I can claim to be two degrees of separation from Dr. Mandelbrot. For me, it is an honor just to claim such a superficial relationship to greatness.

Dr. Mandelbrot at the 2008 Ig Nobel Awards with Fractal Journey's image

 Dr. Mandelbrot at the 2009 Ig Nobel Awards (starts at 29:00) with Fractal Journey's image

Mandelbrot Assemblage

Description
"Mandelbrot Assemblage" is based on the idea in Mandelbrot Birth and Evolution whereby the exponent "n" in the equation z^n+c is manipulated as the principal variable in the animation. However, for this animation, the exponent "n" is decreased from 40 to 2. Furthermore, rather than showing the entire set, the animation zooms in on Seahorse Valley and tracks its evolution as the exponent is reduced to 2. Note that the location is not fixed in this case since the location of Seahorse Valley moves as the exponent is changed.

Music
"Escape" (edited for length) by Dark Flow.

Technical information
Each frame was rendered in luxurious 1920x1080 resolution, strung together at 30 frames per second, and encoded at 16Mbps, making this a Full HD animation worthy of your 1080p flatscreen.

Downloads
Download 1080p MP4 (Highest Quality, 1920x1080 - 253MB)
Download WMV (Medium Quality, 1280x720 - 116MB)

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)

Mandelbrot Ultra Zoom #4: 2.5E194

I believe this is the deepest Mandelbrot zoom video produced to date (November 2008). No pixel interpolation or frame interpolation were used - all images were individually rendered at 640x480 and then strung together at 30 frames per second.
Note that no camera rotation was utilized throughout the animation. This is especially intriguing because the zoom into the targetted filament tip shows the filament rotating around the screen's center. In other words, hidden at the extremity of the filament is a spiral!

Mandelbrot
Final zoom location:
real=-1.2963551381
7303621680
8304477845
2822662624
4803862985
5679928775
8134023909
7541015237
4968874495
7013280950
8921264237
1849205069
1873930630
0129984443
1327669662
9091695392
5715912473
5766218195
3641356251
6581747800
63
img=0.4418516057
3519660121
2848580174
9869488384
9923969742
4758901550
7705711715
9588719169
1529341962
7212288799
9691678065
6481371825
1021509265
0641919732
0221562977
4396782935
1836205354
4727941073
7461632018
1517184948
375
magn=2.514908E194
maximum iterations=1,000,000

Download WMV (640x480 medium quality - 86MB)
Download MP4 (640x480 high quality - 95MB)
Download WMV (640x480 full quality - 275MB)

Mandelbrot at the 2008 Ig Nobel Prizes

Making an appearance at the 2008 Ig Nobel Awards is Fractal Journey's own Mandelbrot set image, originally posted here.


Who is that standing center stage?

It's Doctor Mandelbrot himself! Thanks to Geri Sullivan. Watch the entire 2008 Ig Nobel Prizes ceremony here.

Mandelbrot Ultra Zoom #3: 1.1E101

Mandelbrot
Final zoom location:
real=-1.5752046532
8054518627
7209903318
4298627716
1997610841
0897527488
6072417169
2842426068
8170553920
8484631327
9584803247
5
img=0.0173616212
6272928184
8431301085
0175044293
8051875985
9190469582
1406242723
7361755591
1001831187
2512274494
6906225339
42
magn=1.3293492E101

Download WMV (640x480 full quality - 60MB)
Download WMV (640x480 medium quality - 12MB)

Thunder Front

Mandelbrot
real=-1.2963551381
7303621680
8304477845
2822662624
4803862985
5679928775
8134023909
7541015237
4968874495
7026302523
455
img=0.4418516057
3519660121
2848580174
9869488384
9923969742
4758901550
7705711715
9588719169
1529341962
7209673773
122
magn=8.7793873E92

Stand-off

Mandelbrot
real=0.2500000011222610427628
img=0
magn=1.3800134E13