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Author Topic: Magnum Opus Ex - 3132 Zooms  (Read 1788 times)
Description: A giant X formation, made up of smaller X formations, each made up of tiny Xs
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stardust4ever
Fractal Bachius
*
Posts: 513



« on: December 22, 2011, 11:32:04 PM »

================================
Good news! Fractal is now twice as big! I'm dong a render at 3200x3200 pixels, which is now 25% complete, so I scaled it to 1600 pixels and uploaded the bigger version. The entire thing should take 36 days, 9 days of which are already finished. Enjoy! afro


http://stardust4ever.deviantart.com/art/Magnum-Opus-Ex-3132-6-Zooms-Bigger-1600-274474754

 Smiling Mandelbrot Magnum Opus is Latin for "great work"

It's finally here! It's been my goal for a long time to produce a fractal render consisting of a large X made up of smaller Xs which are made up of tiny X formations. That's an X made up of Xs made up of Xs. See my Reactor Core post for a better explaination of the "X made up of Xs" concept and what inspired me to start searching these formations:
http://stardust4ever.deviantart.com/art/XX-Reactor-Core-Deep-Zoom-131573460

The large X object consists of an X shape in the center consisting of 128 tiny X chromosomes (32 on each arm). Each arm of the large X also contains three smaller X formations, and a bent fragment at the tip, the fragment being too small to really see at this resolution. Each of these 12 smaller Xs contains 64 tiny X chromosomes, 16 on each arm. The four bent fragments on the tips of the Monster-sized X formation each contain a single row of 32 X-chromosomes.

Now to add everything up:
(128 x 1) + (64 x 12) + (32 x 4)
= 1024 tiny little X chromosomes!!!

Because the Mandelbrot fractal is binary, the number of features will always add up to a binary power, 1024 being 2^10. Because each chromosome actually has four arms, the actual number of arms at the lowest level is 4096, or 2^ 12.

So it required a total of 12 periodic doublings to produce the required 4096 arms. Most of those required me to leave the centroid of the fractal, which increases the zoom depth by about 50% deeper and doubles the iteration count. Considering it takes the CPU four times as long to calculate iterations at double the zoom depth, that's quite an expensive undertaiking. Someday I would like to make a print of this by rendering it at 4800 pixels. If my estimations are correct, that will take 59 days, or practically two months to complete. Sometime I plan on upgrading my computer system to an AMD 8150FX CPU (8 integer cores and higher clocks) and a Windows 7 64-bit upgrade from Vista (clean install). Someday when I render this image at a much higher resolution, I will update this post and enable prints to be made.

Post-processing: I have developed a technique for achieving an Anti-aliased look in postwork, by rotating the image around the center pixel and blending them together. For a deep-zoom render with four-fold symmetry, that produces a noticeable improvement in image quality. I'll probably do a post about my technique in fractalforums.com later.

===========================================
Fractal Extreme 2.20 64-bit
Phenom II X4 955 Stock (3.2 Ghz x 4 cores)

Mandelbrot Fractal
800x800 Pixels (no anti-alias)
There is some minor Anti-Alias effect performed in postwork
2 days, 8 hours, 42 minutes
3132.7 Zooms (Approx. 1e-943)
Average Iteration Depth 377,140 /pixel
Total Iterations: 241,369,879,611
Guessed Pixels: Zero

Complex Coordinates:

Cr=
-1.4797962709017600244252799347704115256455510544325995179098076328242862544039075945268884660999628050229751964725497716818312344916955598525839552049861977622938727694748069039955642590406675685997700941126379378570821987561050974456193507569667937931144674320329377993465740144619572026488907382726758104299281925571396606196002960095648852803940011013602573467404942350378153725402938676297434487740893628746489527148378347572616696479155070553056741269846567113187869309530709506083704618952199193376646174337372933529682317495830617582584225996626047220980000003146661160274360111758949932113090681591627736792074508141555030836148272902213632440890171948598870366036119178098168002124472931199675575978515630666649298127196398018688410935222010983880806908352014011077759074249160660588531969863434518905762067484478748868928548778376772438405496400757729996218309016311245625992087187905884917840497006166276051816501705665425555290511990241

Ci=
+0.0011994439528134477462819732333744684445603141141325383620375692056574222167395645214711191076264533309963650679870881466636399967159398318191522486180422558246522689182996308975253866380294287064739208983585061954947980921751709470565080051258981884554765133419312569632099457685179999650016670762993336446844236778034215257672625848788694460282069039665644332180750510211229167948001409358429457822408318525728674579307646027308487673214350326307950188279884353995019301464652536433246988196260720509486592586535111295053754256454877702698366854337740431376220361692073855167521762312416027439765959720756033204080063897947492796559163545415397827454620231617310642320676741985492863616183030871530459422071478512538948407624933074421814042111671749281862544244133767582340846778717570291171721347943794724343146961916816182641403228394362447643718567728423739369698615777094087260365474691300114179641910688342217153247665225738231917222640683
==========================================

My CPU is currently busy cooking up a larger render at 3200x3200 pixels. On my current setup, it will take about 35 days to complete. This was NOT an easy object to find!
« Last Edit: December 29, 2011, 01:13:29 PM by stardust4ever, Reason: larger version uploaded » Logged
Pauldelbrot
Fractal Senior
******
Posts: 2592



pderbyshire2
« Reply #1 on: December 23, 2011, 12:23:19 AM »

Repeating Zooming Self-Silimilar Thumb Up, by Craig
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huminado
Guest
« Reply #2 on: December 24, 2011, 06:50:23 AM »

This is very cool especially the chromosomes!

Post-processing: I have developed a technique for achieving an Anti-aliased look in postwork, by rotating the image around the center pixel and blending them together. For a deep-zoom render with four-fold symmetry, that produces a noticeable improvement in image quality. I'll probably do a post about my technique in fractalforums.com later.

Looking forward to reading this.
Logged
aluminumstudios
Conqueror
*******
Posts: 135


« Reply #3 on: December 28, 2011, 12:58:19 PM »

That is really, REALLY awesome.  It's a stunning picture and really cool that you were hunting for something specific. Yes !!
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stardust4ever
Fractal Bachius
*
Posts: 513



« Reply #4 on: December 29, 2011, 01:10:08 PM »

Hey, thanks! Random Zooms can make interesting videos, but generally create boring stills. Methodological Zooming can create some extremely stunning and intricate patterns, but the iteration depth and zoom levels can skyrocket! Every time you pick a new inflection point outside the centroid, you have to pass through virtually every "feature" you've already seen along the way. The original pattern eventually doubles around the centroid of the inflection point, but the zoom depth can be up to 50% deeper (depending on how developed the "feature" that you zoom into the centroid of), with double the iterations per pixel. If you double the image by zooming into the centroid, going from twofold symmetry to fourfold symmetry, the penalty is significantly less: 16.7 percent deeper zoom depth and 50 percent more iterations.

================================
Good news! Fractal is now twice as big! I'm dong a render at 3200x3200 pixels, which is now 25% complete, so I scaled it to 1600 pixels and uploaded the bigger version. The entire thing should take 36 days, 9 days of which are already finished. Enjoy! afro
Logged
zonepatcher
Conqueror
*******
Posts: 145


« Reply #5 on: January 03, 2012, 07:23:11 AM »

powerful n potent
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