April 30, 2011

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

10 comments:

cosmic matrix said...

OH MY GOD thank you so much, as i'm sure you know this stuff is pretty significant.

i can't watch these without holding on to my chair.

the quality and depth of these is astonishing and you were very to clever to do what you did.

nice! hey check out cosmicmatrixx.blogspot.com for my music, if you like!

Ян said...

Have you uploaded it to same fileshare site with better quality than on youtube, or youtube bitrate is enough already?

Orson said...

The YouTube version is as good as the original due to some upsampling. Considering this is a "blooper", I probably will not be working on version for downloading.

Matteo Monti said...

Hi! Just one question: I see that you zoomed on a very particular point.. Its coordinates are very long.. only I wonder: HOW did you calculate the coordinates of such a special point??
(VERY nice work!!)

Orson said...

I did not calculate the coordinate. Prior to rendering this, I spent time browsing the Mandelbrot set looking for an interesting place to zoom into. As much time as it took to render this video, I spent almost as much time browsing for an interesting point.

karatedog said...

What technique do you use to avoid banding in the colors?

martinsimeovgeo@yahoo.it said...

i noticed that the fractal answers you in base of your chouces

the first choices leave a more significative effect on the behavior

for example, i first noticed that from the first branch (where was a needle)
you became zoming into a crossing of tho branches in 0:46
and in that timw you have outdated other 46 crossings on the firs branch (if we count only the bigger crossing in the screen at the time X.XX)

afther this

EACH OTHER CHANGE IN THE STATEMENT
OCCURRED ONLY afther 46 branch crossings in the whole zoom

you chosen to change the type of part, and afther this, the fractal reproposed you all other changes agan afther 46 crossings!!!!
for example, from 2 to 4 branches he reproposed you 46 crosssings for all branches before duplicate the number

if you noticed also all the points where you changed the zooming center involved different new effects that not disappeared but superimposed on the other

i noticed that the fractal proposed you every change only past 46 crossings
AND that afther 46 changes you was forced to chose another way by appearing the black mandelbrot set

between two mandelbrot sets he forced you to zoom 46 changes distanced themselves by 46 crossings on the branches
in thi times, the behavior is prevedible and regular, but when you are foced tho chose one direction when encounter the black set, the behavior maintans the structure, but overlaps the changed behavior on the pre-existent and create a new behavior that consider both

in the video you encountered 4 times the black set

i'm very curious to know what he will do when you encounter the 47° black set...

zooming that i'm asking is excessive, but you can try to see what happens if you change fron the first branch in the first cross afther only 10 crossings (and not 47) :D

you will see the black set 10 times very easily and you will have an idea what happens at the 11° and what was able your video to show if you zoom on the 47° black set

martinsimeonovgeo@yahoo.it said...

i'm talking about this video

http://www.youtube.com/watch?v=0jGaio87u3A&feature=related

Manuel Sánchez Carrilero said...

Please:

Someone could explain to me how to handle such a large number of digits (200 or more),
such as is made in the computation of the Mandelbrot set zoom.
The usual codes handle 16 to 28 digits maximun.
It is a mystery to me!

Thank you

Orson Wang said...

Arbitrary precision math: https://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic