(Attn: stardust4ever) Magnum Opus Ex full zoom

[Kalles Fraktaler]

Nice to see that you are back stardust!
I hope you will discover the amazing findings by mrflay (K.I Martin, no longer active) completed by Pauldelbrot! And I hope you want to try my implementation of it, Kalles Fraktaler 2, which is more than 100 times faster than traditional programs on deep locations. Or Mandel Machine which is up to another 100 times faster than KF on some locations, but unfortunately not yet complete.

[stardust4ever]

How does this new program work? I'm skeptical that it's really 100x faster than Fractal Extreme.

Fractal Extreme was for years the fastest Fractal Rendering software out there because it utilized 64-bit longnum integer math routines written in x86-64 assembly, with various redundant calculations removed from the equation. Most competing fractal proggies used 32-bit calcs (4x penalty) written in a slow language like C (more penalty) with little low level speed optimizations (again roughly 4x penalty). I have often wondered, however, if faster implementations were possible. Julias and Perturbations have interesting properties when set to a point many many zooms deep within the set. I tried doing (0,0) Julia zooms with the seed set to the final minibrot, which allows virtually identical formations with less repitition at lower zoom depths, but it required higher precision that the software allowed at current zoom level, causing the render to fail.

Another thing I've thought about, once you're far away from any minibrots, and with the type of images I've been rendering, zooming into the centroid will double and quadruple the surrounding patterns, ultimately leading to a minibrot. Zooming into a point off of the centroid eventually leads to a repeat of all the patterns previously seen, until ultimately leading to an image resulting from the original pattern being wrapped twice around the chosen point of inflection.

Ultimately all of the intricate patterns I have created were based on blazing trails based upon te above principal. I propose it would be possible to render such detailed Mandelbrot patterns, not by zooming 1000s of zooms deep, but simply by selectively rendering key points around such a feature and distorting the shape in such a mnner as to emulate the natural contortions present within the Mandelbrot set.

To better describe this concept, think of zoom movies not as video files consisting of vast numbers of 2D frames, but as a cyclindrical tube. The tube is essentially a bitmap image of X pixels in width (distance equal to 2PI or 360 degrees) and arbitrary height. Moving down the bitmap equates to deeper zoom, moving up equates to shallow. The height is a log scale, so features get progressively larger or smaller. Start to finish from mandelbrot to minibrot you have your entire zoom sequence mapped out on a 2D cylindrical plane. Take a cross section of this plane 50% between the start and finish, and compare it to a slice 75% between start and finish. The pattern will be the same but it wraps around the zoom cylinder twice instead of once. Furthermore, if we go 87.5% to the end or 7/8, the pattern will repeat around the zoom cylinder four times. At 15/16 to the end, 8 times. 31/32 to the end, 16 times. The features become smaller and smaller until it reaches the event horizon, the minibrot which is like a black hole in that even an infinite amount of iterations can escape it's influence.

Now that we can visualize the zoom sequence as a flat but finite cylinder with repeating patterns rather than a large fractal plane with infinitely small features, the mystery of the Mandelbrot is largely unraveled. So, since the patterns repeat ad-infinitum, it should be possible to distort the ether that is the Mandelbrot Set at relatively low zoom depths, and remap these points to duplicate the itricate imagery found much deeper within the set, without doing the inane, tedious, and computationally astronomical work of zooming thousands of frames deep calculating millions of iterations per pixel.

I hope that makes sense. Just contort the set to produce whatever feature you want to create, then render just that, rather than brute force the pattern by relentless zooming. Sit and watch the entire 30 minute video and ask yourself if zooming through the exact same patterns countless times is the best strategy to create/locate these intricate formations. No matter how powerful the computer, you'll always hit a brick wall.

That was why I gave up on the deep zoom thing. I figured there's got to be a better way of doing it than the old iteration loop until bailout. Just my luck I leave the scene for a moment and somebody discovers some new rendering technique. Just some food for thought. Suns coming up. Gotta get some sleep now.

[stardust4ever]

Magnum Opus Lite (the slightly shorter zoom video I've been sitting on since April 2012) is live:
<a href="http://www.youtube.com/v/0WChGAK_mYg&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/0WChGAK_mYg&rel=1&fs=1&hd=1</a>

EDIT: For some unknown reason, the forum is borking the standard Youtube url. Try this version instead:
<a href="http://www.youtube.com/v/0WChGAK&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/0WChGAK&rel=1&fs=1&hd=1</a>

[Kalles Fraktaler]

How does this new program work? I'm skeptical that it's really 100x faster than Fractal Extreme.

We have used this image, zoomed to 6e141, as benchmark:
http://www.fractalforums.com/images-showcase-(rate-my-fractal)/tick-tock/

On my machine Fractal extreme is rendering it in 10 minutes in 640x360.
Kalles Fraktaler is rendering it in 4.5 seconds - that is 133 times faster.
And Mandel Machine is rendering it within 1 second, i.e. more than 600 times faster!

If you want the details of the new rendering method look at this thread
http://www.fractalforums.com/index.php?topic=15559.0

It is a very long thread, so in short - only one pixel is calculated with full precision and used as a reference to calculate all other pixels in the image with only hardware double precision.
Further a truncated Taylor Series can approximate a starting value for the low precision pixels that enables a significant amount of iterations to be skipped.
But unless this reference pixel is carefully selected and the pixel's differences in iteration counts are low, this rendering method cause errors because the double precision is not enough.
That issue was solved by Pauldelbrot that discovered that the orbits of the reference and the low precision pixels are "snapped together", so by measuring the relative distance between them the incorrect pixels can be identified and recalculated with additional references.
http://www.fractalforums.com/index.php?topic=18908.0

[stardust4ever]

We have used this image, zoomed to 6e141, as benchmark:
http://www.fractalforums.com/images-showcase-(rate-my-fractal)/tick-tock/

On my machine Fractal extreme is rendering it in 10 minutes in 640x360.
Kalles Fraktaler is rendering it in 4.5 seconds - that is 133 times faster.
And Mandel Machine is rendering it within 1 second, i.e. more than 600 times faster!

If you want the details of the new rendering method look at this thread
http://www.fractalforums.com/index.php?topic=15559.0

It is a very long thread, so in short - only one pixel is calculated with full precision and used as a reference to calculate all other pixels in the image with only hardware double precision.
Further a truncated Taylor Series can approximate a starting value for the low precision pixels that enables a significant amount of iterations to be skipped.
But unless this reference pixel is carefully selected and the pixel's differences in iteration counts are low, this rendering method cause errors because the double precision is not enough.
That issue was solved by Pauldelbrot that discovered that the orbits of the reference and the low precision pixels are "snapped together", so by measuring the relative distance between them the incorrect pixels can be identified and recalculated with additional references.
http://www.fractalforums.com/index.php?topic=18908.0

This is an awesome development! I downloaded Kalles Fraktaler and explored well past e600 or so. I was watching the images render on the screen and there is definitely something different going on with the pixels. The iteration count nearly instantly goes up to some amount, then jumps again filling the holes as it renders. It's as if I'm watching the iteration count increase as the image renders. Just the interface seems a little clunky and it will take a bit getting used to a new software interface after using the smoothe Fractal Extreme for so long. Gotta check out Mandel Machine as well...

 

[Kalles Fraktaler]

Thanks. Yeah, I haven't used fx much so I did many things differently.
And I do not want to belittle fx since I am certainly not able to do it faster in the old way, and I know it is indeed possible to do it much faster in the new way, as Mandel machine implemented in assembler instead of C++ and utilizing SIMD for parallel operations within each thread.
But so far Kalles Fraktaler is the only available program that solves all the glitches automatically.
I might implement SIMD myself one day, but it requires restructuring a big part of my program and debugging is very time consuming

[stardust4ever]

Well I've gotten off my Kester and installed Kalles Fraktaler. I rendered a frame of Magnum Opus Ex formation at 1920x1080. Took an hour on my quad core AMD laptop. Is there a way to change the aspect ratio as it appears stuck in 16x9. I'm gonna do some heavy rendering on my older but massive 8-core rig and see what I can churn out. It's got 4.2Ghz OC and is about 3x as fast with FX as my laptop.

[Kalles Fraktaler]

((1920*1080)/(3200*3200))*(28*24+18) / 1 = 140 times faster, not considering different hardware. Cool

Arbitrary ratio is not currently possible, because the main target is movies, and that it requires a lot of work.
But it is indeed possible...?

Addition: KF is using long double on locations deeper than e600 which is about 3.5 times slower. Botond has shown that after the approximation ordinary doubles can be used for this location. Further much more iterations can be skipped if more terms is used for approximation. And SIMD would of course speed up with the same amount as the grouping sizes. So it is possible to render this particular location 10,000 times faster than FX!!

[stardust4ever]

Addition: KF is using long double on locations deeper than e600 which is about 3.5 times slower. Botond has shown that after the approximation ordinary doubles can be used for this location. Further much more iterations can be skipped if more terms is used for approximation. And SIMD would of course speed up with the same amount as the grouping sizes. So it is possible to render this particular location 10,000 times faster than FX!!

My 8-core beast rendered this image (3610 zooms) in 32 seconds using Mandel Machine. Days on FX literally became seconds!!!
http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/pterodactyl-vertebrae/

Sadly Mandel Machine caps at 3700 zooms so I am continuing my quest for deeper images in Kalles Fraktaler. But without aspect ratio adjustment or rotation, sometimes I get stuck, for instance if I'm trying to render an oblong shape that happens to be vertically oriented.

Also zoom progress is somewhat slow because I have to wait for the feeder pixel to compute with every zoom advance.

[stardust4ever]

I'm probably done with the X motif for now (yeah said that one before, ha!), but to anyone interested, have a look at this little number...

"Seven Ex Magnum" - seven repetitions of the Magnum Opus Lite feature. 5210 zooms deep in Mandel Machine!

Fractal Forums (parameter file also available for download):
http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/triple-ex-magnum/msg76128/#msg76128

DeviantArt (high quality view/download):
http://stardust4ever.deviantart.com/art/Seven-Ex-Magnum-475692041

It's weird in a way how images that used to take days, weeks, or months can now be rendered in minutes. Finding an object now takes far longer than rendering it. Like, the first time when I spent over a month rendering the Magnum Opus Ex image, and even upgraded my PC in the interim, it really meant something to finally see it realized. In truth, I have Magnum Opus Ex (X of X of Xs) framed on my living room wall next to XX Reactor Core (the original X of Xs). Now that it seems like we can just zoom as deep as we want to, and get instant gratification for doing so, some of the magic is lost. Feels almost like cheating in a way...

I guess what one really needs to ask, is "Where do I go from here?" Abs() Mandelbrot formula variants?? 3D Mandelbulb/Mandelbox???

Oh and one final thing, thanks for getting me back into the fractal scene.

I just gotta contemplate what to do with all that extra speed boost...

[Botond Kósa]

It's weird in a way how images that used to take days, weeks, or months can now be rendered in minutes. Finding an object now takes far longer than rendering it. Like, the first time when I spent over a month rendering the Magnum Opus Ex image, and even upgraded my PC in the interim, it really meant something to finally see it realized. In truth, I have Magnum Opus Ex (X of X of Xs) framed on my living room wall next to XX Reactor Core (the original X of Xs). Now that it seems like we can just zoom as deep as we want to, and get instant gratification for doing so, some of the magic is lost. Feels almost like cheating in a way...

I get what you mean. It must be like collecting stamps as a child and one day receiving a briefcase from your uncle, full of stamps... 

But it can also be seen the other way. By rendering time not being a limiting factor, the creation of interesting images depends more on one's creativity and aesthetic skills rather than patience. We have seen too many "Deepest zoom ever" animations and stills from deep but boring regions of the Mandelbrot set.

[Botond Kósa]

I'm probably done with the X motif for now (yeah said that one before, ha!)...

You also said that when posting your XXX Cold Fusion Cell image (http://stardust4ever.deviantart.com/art/XXX-Cold-Fusion-Cell-154728253), just to come with Magnum Opus Ex later...   

[stardust4ever]

Magnum Opus Ex started with an almost identical location to the Cold Fusion Cell render.

I can continue to zoom into the center of the Seven Magnum formation which will give me a rough "X of Xs of Xs of Xs" shape, but the central formation would have eight arms instead of four.

Or if I back up to the Triple Magnum render and use the edge of the fragment at the end instead of the center, it will eventually create something similar in concept to the Magnum Opus Ex fractal, but it will be an X of Xs of Xs of Xs. One caveat is due to the zoom methods, the center formation will have a big X in the center, then 3 smaller X of Xs, then a bend snake, then three more X of Xs, then a tiny bent fragment on the edge. The X of Xs of Xs of Xs formation would then have the three standard X of Xs of Xs (Magnum Opus Lite shapes) in each arm (12 total) followed by the bend fragments comprised of X of Xs formations ('XXX/XXX') on the edge of each leg. The stripe half way up each leg will be an artifact of the methods I used to create the Magnum Opus fractal and cannot be corrected at this point without unwinding and choosing a completely different zoom path. The image I have envisioned will need to expand the maximum zoom depth of Mandel Machine to at least 7200 zoom levels, ironically barely within the zoom limits of the original Fractal Extreme. I imagine it would also be possible to use Kalles Fraktaler, but by guesstimation the render would likely take several days to about a week to complete. Mandel Machine would take a couple hours tops.

At some point however, the images will become so intricate that much of details will be lost unless the image is rendered to gigantic resolutions.

[Kalles Fraktaler]

Here is one way to go from now:
http://www.youtube.com/channel/UCupBhu5TVx3RNK3iUIdeVlg

This guy have made some amazing movies with my program. To bad YouTube has too hard compression. Because I really like patterns that appears over the spirals because the palette is synced with them.
I can hardly imagine what we can do with references with billions of iterations and perturbation, series approximation, SIMD, glitch solving and carefully customized coloring all together
But one thing is for sure - depth is not so fascinating anymore.

So please keep zooming

Here is a little attempt also from me
<a href="http://www.youtube.com/v/Cik4y4s-HIM&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Cik4y4s-HIM&rel=1&fs=1&hd=1</a>

[stardust4ever]

But one thing is for sure - depth is not so fascinating anymore.

So please keep zooming

Here is a little attempt also from me
<a href="http://www.youtube.com/v/Cik4y4s-HIM&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Cik4y4s-HIM&rel=1&fs=1&hd=1</a>

Yeah depth only impresses so much. I have pretty much mastered the art of multi-replicating shapes, which can create mind-blowingly intricate stills, but now I need to branch out by picking different styles of inflection points. Zeep zoom movies of these multireplication points are actually boring and repetitive. Some of the better zoom movies are actually made by whimsically picking seemingly random locations for inflection points, creating a varied look throughout the whole zoom video.

And yes, I'll keep zooming!