*Continued* SuperFractalThing: Arbitrary precision mandelbrot set rendering in Java.

[stardust4ever]

Have you tried this location in MM with "ignore small add-ends" switched off?
Have you tried it with less terms for approximation?

Well no, but the fractal itself isn't glitched up persay, it just isn't calculating the unsolved areas. Normally, these areas get fixed with second, third, and so on passes. For some reason Mandel Machine doesn't seem to do this past around 6000 or so zooms. But to answer your question, no, I did not attempt to use this mode.

[Kalles Fraktaler]

Well no, but the fractal itself isn't glitched up persay, it just isn't calculating the unsolved areas. Normally, these areas get fixed with second, third, and so on passes. For some reason Mandel Machine doesn't seem to do this past around 6000 or so zooms. But to answer your question, no, I did not attempt to use this mode.

I think these are not the ordinary glitches but comes from ignore small add-ends. I think I had the same kind of issues and eventually I gave up that track of optimization. When to include or not to include add-ends is hard to generalize, the deeper and closer to minibrot you get the more sensitive it gets.

[stardust4ever]

I think these are not the ordinary glitches but comes from ignore small add-ends. I think I had the same kind of issues and eventually I gave up that track of optimization. When to include or not to include add-ends is hard to generalize, the deeper and closer to minibrot you get the more sensitive it gets.

It is unfortunate too. The "small addends" start to get nasty with the 4th and 5th order equations as you demonstrated in another thread. Maybe if the squares were included in calculations but not the 3rd and 4th power terms? One could check the magnitude of the addends and only calculate them if they are larger than the current precision level. However estimating their magnitude prior to calculation may not save much time when dealing in floats or doubles.

I get that as the orbits slowly escape, the delta values become larger with time so that these "small addends" may not be so insignificant as the orbit approaches it's escape trajectory. You can only get away with skipping so many computations before the integrity of the render is compromised. And zoom movies full of glitches are no fun to fix. Sometimes I simply leave them in when it rarely happens.

[quaz0r]

its not that fantastic of an optimization anyhow 

[Kalles Fraktaler]

I 100% agree, and have been following the SFT / perturbation thing since the beginning, spoke with the author of UltraFractal about his investigations of the technique in 2014 at the Fractal Art Symposium... my comment from 2013 still stands:

"Nevertheless, the real issue I have with this method is that it's not a true acceleration for the same computation. It's a kind of approximation, and the deviation from the "true" result is essentially impossible to quantify since it's a chaotic system. So it's something like apples and oranges comparison, no?"

I don't see how trading computer processing power for human effort (looking for glitches) is a winning strategy, or even a sure one - people have missed glitches before, and until there's some kind of proof of correctness (itself more difficult to compute than a reference image with direct iteration) the resulting image quality is dependent on the patience and eyesight of the person doing the rendering.

UltraFractal is promised to have perturbation in it's next release.
When is Chaotica going to have perturbation?

[stardust4ever]

UltraFractal is promised to have perturbation in it's next release.
When is Chaotica going to have perturbation?

That is news. I'll even buy an "upgrade" if they pull this off in UF6.

Better yet is they can implement perturbation with some of the public databases without reworking them. A lot of the equations are "junk" though. Interest in some equations like the Lambda and others is mostly academic however since any amount of deep zooming will reveal it's just the period two bulb of the Mandelbrot set mirrored.

[quaz0r]

as far as i can tell with what everyone has been doing with series approximation thus far, it all seems like one big exercise in taking a wild stab in the dark and just hoping for the best:  checking against arbitrary points to determine how many iterations to skip for all points and just hoping it all works out in the end, and not even having a proper check to begin with for when to bail on the series approximation.  checking whether terms outgrow other terms by some arbitrary amount, wtf is that exactly?  can that be proven to be a correct and comprehensive methodology?  as far as i can tell it is basically just something one guy pulled out of thin air one day and it seems to kind of work and nobody has really given it much thought beyond that.  noting also that this guy's program, as much good as can be said for it, has always been buggy and glitchy, and is now abandonware.

i was just looking again at knighty's post for calculating the error in the series approximation, and it actually doesnt look all that costly.  though it seems you still are left with the problem of checking against arbitrary points and hoping for the best.  could there be any way to improve that aspect?

[Kalles Fraktaler]

i was just looking again at knighty's formula for calculating the error in the series approximation, and it actually doesnt look that costly.  if i read the post correctly there is no testing against points, so if it indeed works then it should be solid.  that would be fantastic.  as far as i can tell with what everyone has been doing with series approximation thus far, it all seems like one big exercise in taking a wild stab in the dark and just hoping for the best:  checking against arbitrary points to determine how many iterations to skip for all points and just hoping it all works out in the end, and not even having a proper check to begin with for when to bail on the series approximation.  checking whether terms outgrow other terms by some arbitrary amount, wtf is that exactly?  can that be proven to be a correct and comprehensive methodology?  as far as i can tell it is basically just something one guy pulled out of thin air one day and it seems to kind of work and nobody has really given it much thought beyond that.  noting also that this guy's program, as much good as can be said for it, has always been buggy and glitchy, and is now abandonware.

Do you mean that K.I.Martin's Superfractalthing is "abandonware"?

[quaz0r]

i was referring to botond and his mandelmachine.  did martin ever talk about the specifics of his implementation of the series stuff?  i havent used SFT much, though i seem to recall people reporting that it was rather glitchy and incomplete, and i think he stopped working on it before the advent of glitch detection and any other advances that have been made here on the forums.  from the looks of his sourceforge page, it doesnt look like there has been any real development on it since he first introduced it.

since nobody else seems interested, i guess i'll try implementing knighty's wall of math and report back with any success stories, though i dont know if i will be able to decipher it.  it would be neat if you guys could dumb it down once in a while for us non-math folk.    for instance, i dont know what R₀ should be.  i dont know what E is.  i dont know what this means:  "E = [0,1]*exp(i*]-infinity, +infinity[".  and im not sure how all this is supposed to be used either.  is this intended for the checking against arbitrary points to determine the number of iterations to then skip for all points in the image, like how people have been doing?  or is this R thing supposed to be used during the initialization of each point, where if an error tolerance is exceeded you just try that point again later with another reference point?

in any case, it seems to me that the only really proper way of doing things would be to check every point for what iteration to start on, but that would take too long so nobody is ever going to do it that way.  can anyone prove / even just say with some legitimate degree of confidence that arbitrarily picking a starting point for all points can always produce correct results, and will never result in any points starting too late?  keeping in mind that going too far with series approximation can result in incorrect results that will not get caught by the perturbation-glitch detection.

[stardust4ever]

Mandel Machine may be abandonware (hasn't been updated since 2014 I believe) but it is fast and I have been able to render some amazing images with it. Both my contest winners were Mandel Machine renders.

However, if Botond is still around, it would do a lot of goodwill to the community to release the source under GPL if he doesn't want to maintain it any more.

[Pauldelbrot]

Mandel Machine may be abandonware (hasn't been updated since 2014 I believe) but it is fast and I have been able to render some amazing images with it. Both my contest winners were Mandel Machine renders.

However, if Botond is still around, it would do a lot of goodwill to the community to release the source under GPL if he doesn't want to maintain it any more.

Concur.

[Kalles Fraktaler]

Mandel Machine may be abandonware (hasn't been updated since 2014 I believe) but it is fast and I have been able to render some amazing images with it. Both my contest winners were Mandel Machine renders.

However, if Botond is still around, it would do a lot of goodwill to the community to release the source under GPL if he doesn't want to maintain it any more.

I believe the source is available on his site.
(tons of assembler...  )

[stardust4ever]

I believe the source is available on his site.
(tons of assembler...  )

Assembly would explain why it's so fast. If Mandel Machine were a car and we were caught driving it, they'd have given us all speeding tickets...

[Kalles Fraktaler]

Assembly would explain why it's so fast. If Mandel Machine were a car and we were caught driving it, they'd have given us all speeding tickets...

With this methaphore, we would be able to turn in almost all curves, except a few... 

[stardust4ever]

 

With this methaphore, we would be able to turn in almost all curves, except a few... 

Automatic glitch correction is analogous to tracktion control. Occasionally you still glitch, er crash...