Fractalforums

Kalles Fraktaler 2 + GMP homepage: https://mathr.co.uk/kf/kf.html

As the orginal upstream author says:

Want to create DEEP Mandelbrot fractals 100 times faster than the commercial programs, for FREE? One hour or one minute? Three months or one day? Try Kalles Fraktaler!

I forked the code and swapped out the custom arbitrary precision floating point code for the highly optimized GMP library, making it even faster.

new version 2.12.2 available to download, lots of new features, please test to check I didn't break any of the more unusual formulas in the process of massaging formula XML so the preprocessor could work its magic.  Changes:

- PNG image saving support using libpng and zlib; see https://fractalforums.org/index.php?action=gallery;sa=view;id=78 for quality comparison with JPEG
- JPEG default quality to 100 (was 99);
- colouring uses floating point internally to reduce quantisation steps;
- dithering at end of colouring to improve perceptual quality; see https://fractalforums.org/index.php?action=gallery;sa=view;id=80 for quality comparison (view full size for best effect)
- formula.cpp included in source zip so GHC is not needed unless changing formula code;
- optimized diffabs() code: one test Burning Ship location is 7.5% faster;
- preprocessor optimizes reference calculations by floating temporary variable (re)allocations out of the inner loops: one test Burning Ship location is 30% faster;

great to see KF still being improved and worked on.

New version 2.12.3 available:

- multiple differencing methods for distance colouring (thanks to gerrit)
- bugfixes to examine zoom sequence (thanks to Dinkydau and Fractal universe for reporting)
- raised reference count limit from 199 to 10000, default remains 69
- settable additional reference count in examine zoom sequence, default remains 10

Thanks also on the new forum for this.

Is there any reason KF does not support true distance estimation using perturbation methods?
A similar formula for dz involving only "small" quantities seems possible. I'm sure the devil is in the details which I don't know.


 

Perturbation and series approximation do indeed work with the derivatives needed for true distance estimation, I have some side projects that do it for quadratic Mandelbrot set.

Adding it to KF would be a lot of work, in part because there are over 50 formulas to consider, although some might not have analytical DE with derivatives (Burning Ship with abs(), etc).

If/when adding it, it would be necessary to make the derivative calculations (including series approximation) optional, to avoid slowing down rendering when it isn't needed. Same for memory allocation for the result.

I tried reading a kfb file, extract counts-trans, compute the numerical gradient, then compute the entropy and plot.

The result shows faintly the boundaries between the iteration bands.

If I recompute the same thing from scratch using old-fashioned slow methods,  I do not get these bands, unless I set the escape radius too low.

What is the value of the escape radius in KF  ("high bailout")?

Edit: I can reproduce the problem at bailout |z| = 100 or less.
 

Perturbation and series approximation do indeed work with the derivatives needed for true distance estimation, I have some side projects that do it for quadratic Mandelbrot set.

Adding it to KF would be a lot of work, in part because there are over 50 formulas to consider, although some might not have analytical DE with derivatives (Burning Ship with abs(), etc).

If/when adding it, it would be necessary to make the derivative calculations (including series approximation) optional, to avoid slowing down rendering when it isn't needed. Same for memory allocation for the result.

I have never paid much attention to those other fractals. Feature creep according to my purist mind. 
Anyways I think it would be reasonable to have some extra features just for the king of fractals, the M-set.
Is not the newton-raphson  zooming only M-set? I played with the other fractals a bit but never got NR to do anything. So maybe there is a precedent?

Regarding efficiency, I've found to get the gradient based DE to be visually indistinguishable from the analytic DE requires a grid 4 time bigger. That means 16 times more space and time, compared to 2 times for an analytical DE (time is less, about 50% I think).
Of course the GUI programming would be unpleasant: a "do an. DE" special option and then some choices how to render an. DE in the color dialog, which need to be disabled when the special option was not selected. And change the format of the kfb files, making sure not to break the movie maker, aarghh.

While I'm at it, some of the other interesting stuff you've done on the M-set would be really great to incorporate in KF for normal people that don't know how to compile C on Unix.  Have you considered taking over KF more "seriously" using crowdfunding? Not sure if there is a "market" apart from me, but I'll put in 1K if you do.

When creating a zoom sequence I get distorted images, see below. I don't get this in the Kalles distribution 2.11.1.
This makes it into the movie too when assembled.

Re: -0.1689871149278873911097660503676038118745163900005532541510126433401072125433421201418637182399553895504
Im: -1.042370253271613666018000410716463804803767498360356704962779325184161205503626075524139049523435010426575
Zoom: 8.06779400727E80
Iterations: 10000
IterDiv: 1.000000
SmoothMethod: 0
ColorMethod: 5
ColorOffset: 0
Rotate: 0.000000
Ratio: 360.000000
Colors: 255,255,255,254,254,254,254,253,253,254,251,252,254,249,249,253,245,246,253,241,243,252,237,239,252,231,234,251,225,229,250,219,223,249,212,217,248,204,210,247,196,203,246,188,196,245,179,188,244,170,180,243,161,172,242,151,164,240,141,155,239,132,147,238,122,138,237,112,129,235,103,121,234,93,113,233,84,104,232,75,96,231,66,89,230,57,81,229,49,74,228,42,68,227,35,62,226,28,56,225,23,51,225,17,46,224,13,42,224,9,39,223,5,36,223,3,33,223,1,32,223,0,31,222,0,31,222,0,31,222,0,31,222,0,31,222,0,31,221,0,32,221,0,32,220,0,33,220,0,33,219,0,34,218,0,35,217,0,36,216,0,37,215,0,38,214,0,39,213,0,40,212,0,41,211,0,42,209,0,44,208,0,45,207,0,46,206,0,47,205,0,48,203,0,50,202,0,51,201,0,52,200,0,53,199,0,54,198,0,55,197,0,56,196,0,57,195,0,58,194,0,59,193,0,60,193,0,60,192,0,61,192,0,61,191,0,62,191,0,62,191,0,62,191,0,62,190,0,63,190,0,63,190,0,63,190,0,63,190,0,63,189,0,64,189,0,64,188,0,65,188,0,65,187,0,66,186,0,67,185,0,68,184,0,69,183,0,70,182,0,71,181,0,72,180,0,73,179,0,74,177,0,76,176,0,77,175,0,78,174,0,79,173,0,80,171,0,82,170,0,83,169,0,84,168,0,85,167,0,86,166,0,87,165,0,88,164,0,89,163,0,90,162,0,91,161,0,92,161,0,92,160,0,93,160,0,93,159,0,94,159,0,94,159,0,94,159,0,94,158,0,95,158,0,95,158,0,95,158,0,95,158,0,95,157,0,96,157,0,96,156,0,97,155,0,98,155,0,98,154,0,99,153,0,100,152,0,101,151,0,102,150,0,103,149,0,104,148,0,105,147,0,106,145,0,108,144,0,109,143,0,110,142,0,111,140,0,113,139,0,114,138,0,115,137,0,116,136,0,117,135,0,118,134,0,119,133,0,120,132,0,121,131,0,122,130,0,123,129,0,124,129,0,124,128,0,125,128,0,125,127,0,126,127,0,126,127,0,126,127,0,126,126,0,127,126,0,127,126,0,127,126,0,127,126,0,127,125,0,128,125,0,128,124,0,129,123,0,130,123,0,130,122,0,131,121,0,132,120,0,133,119,0,134,118,0,135,117,0,136,116,0,137,115,0,138,113,0,140,112,0,141,111,0,142,110,0,143,108,0,145,107,0,146,106,0,147,105,0,148,104,0,149,103,0,150,102,0,151,101,0,152,100,0,153,99,0,154,98,0,155,97,0,156,97,0,156,96,0,157,96,0,157,95,0,158,95,0,158,95,0,158,95,0,158,94,0,159,94,0,159,94,0,159,94,0,159,94,0,159,93,0,160,93,0,160,92,0,161,91,0,162,91,0,162,90,0,163,89,0,164,88,0,165,87,0,166,86,0,167,85,0,168,84,0,169,82,0,171,81,0,172,80,0,173,79,0,174,78,0,175,76,0,177,75,0,178,74,0,179,73,0,180,72,0,181,71,0,182,70,0,183,69,0,184,68,0,185,67,0,186,66,0,187,65,0,188,65,0,188,64,0,189,64,0,189,63,0,190,63,0,190,63,0,190,63,0,190,62,0,191,62,0,191,62,0,191,62,0,191,62,0,191,61,0,192,61,0,192,60,0,193,59,0,194,59,0,194,58,0,195,57,0,196,56,0,197,55,0,198,54,0,199,53,0,200,52,0,201,50,0,203,49,0,204,48,0,205,47,0,206,46,0,207,44,0,209,43,0,210,42,0,211,41,0,212,40,0,213,39,0,214,38,0,215,37,0,216,36,0,217,35,0,218,34,0,219,33,0,220,33,0,220,32,0,221,32,0,221,31,0,222,31,0,222,31,0,222,31,0,222,30,0,223,30,0,223,30,0,223,30,0,223,30,0,223,29,0,224,29,0,224,28,0,225,27,0,226,27,0,226,26,0,227,25,0,228,24,0,229,23,0,230,22,0,231,21,0,232,20,0,233,19,0,235,18,0,236,16,0,237,15,0,238,14,0,239,13,0,241,12,0,242,11,0,243,9,0,244,8,0,245,7,0,246,6,0,248,5,0,248,4,0,249,4,0,250,3,0,251,2,0,252,1,0,252,1,0,253,0,0,253,0,0,254,0,0,254,0,0,254,0,0,254,0,0,255,0,0,255,0,0,254,0,0,255,0,0,255,0,1,255,0,1,255,0,2,255,0,3,255,0,3,255,0,4,255,0,5,255,0,6,255,0,7,255,0,8,255,0,9,255,0,10,255,0,11,255,0,12,255,0,14,255,0,15,255,0,16,255,0,17,255,0,18,255,0,19,255,0,21,255,0,22,255,0,23,255,0,24,255,0,25,255,0,26,255,0,26,255,0,27,255,0,28,255,0,29,255,0,29,255,0,30,255,0,30,255,0,30,255,0,30,255,0,30,255,0,31,255,0,31,255,0,31,255,0,31,255,0,31,254,0,32,255,0,32,255,0,33,255,0,34,255,0,34,255,0,35,255,0,36,255,0,37,255,0,38,255,0,39,255,0,40,255,0,42,255,0,43,255,0,44,255,0,45,255,0,46,255,0,48,255,0,49,255,0,50,255,0,51,255,0,52,255,0,53,255,0,55,255,0,56,255,0,57,255,0,57,255,0,58,255,0,59,255,0,60,255,0,60,255,0,61,255,0,62,255,0,62,255,0,62,255,0,62,255,0,62,255,0,63,255,0,63,255,0,63,254,0,63,255,0,63,255,0,64,254,0,64,255,0,65,255,0,66,255,0,66,255,0,67,255,0,68,255,0,69,255,0,70,255,0,71,255,0,72,255,0,74,255,0,75,255,0,76,254,0,77,255,0,78,255,0,80,255,0,81,255,0,82,255,0,83,255,0,84,255,0,86,255,0,87,255,0,88,255,0,89,255,0,90,255,0,90,255,0,91,255,0,92,255,0,93,255,0,93,255,0,94,255,0,94,255,0,94,255,0,94,255,0,94,255,0,95,255,0,95,255,0,95,255,0,95,255,0,95,255,0,96,255,0,96,255,0,97,255,0,98,255,0,99,255,0,99,255,0,100,255,0,101,255,0,102,255,0,103,255,0,104,255,0,106,255,0,107,255,0,108,255,0,109,254,0,110,255,0,112,255,0,113,255,0,114,255,0,115,255,0,116,255,0,118,255,0,119,255,0,120,255,0,121,255,0,122,255,0,122,255,0,123,255,0,124,255,0,125,255,0,125,255,0,126,255,0,126,255,0,126,255,0,126,255,0,126,255,0,127,254,0,127,255,0,127,255,0,127,255,0,127,255,0,128,255,0,128,255,0,129,255,0,130,254,0,131,255,0,131,255,0,132,255,0,133,255,0,134,255,0,135,255,0,137,255,0,138,255,0,139,255,0,140,255,0,141,255,0,143,255,0,144,255,0,145,255,0,146,255,0,147,255,0,148,255,0,150,255,0,151,255,0,152,255,0,153,255,0,154,255,0,154,255,0,155,255,0,156,255,0,157,255,0,157,255,0,158,255,0,158,255,0,158,255,0,158,255,0,158,255,0,159,255,0,159,2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Smooth: 1
MultiColor: 0
BlendMC: 0
MultiColors: 
Power: 2
FractalType: 0
Slopes: 0
SlopePower: 50
SlopeRatio: 50
SlopeAngle: 45
imag: 1
real: 1
SeedR: 0
SeedI: 0
FactorAR: 1
FactorAI: 0

I'd prefer it in future if each issue was a separate thread with a (Problem) prefix that could be marked (solved) later.  But for now I reply here:

What is the value of the escape radius in KF  ("high bailout")?

https://code.mathr.co.uk/kalles-fraktaler-2/blob/1be4751fb782af0ec58dda8bbd300475b14c62b3:/fraktal_sft/fraktal_sft.h#l37

#define SMOOTH_BAILOUT 100

https://code.mathr.co.uk/kalles-fraktaler-2/blob/1be4751fb782af0ec58dda8bbd300475b14c62b3:/fraktal_sft/fraktal_sft.cpp#l164

m_nBailout = SMOOTH_BAILOUT;
m_nBailout2 = m_nBailout*m_nBailout;

I can increase it in the next release, to 10,000 or perhaps even 100,000,000.  These increases are by squaring, so it should theoretically change the smoothed iteration count by an integer (I don't think KF uses the escape-radius-independent renormalisation - maybe it should?).

Is not the newton-raphson  zooming only M-set?

Yes M-set only, and the current implementation is even only for power 2 quadratic-M-set.

I put analytical DE on the TODO list.

Have you considered taking over KF more "seriously" using crowdfunding?

I think it's better for my health if I keep working on it as a "hobby" project without external commitments and deadlines...  Maybe I'll reconsider after Brexit when the economy has crashed and I'm more in need of funds...

When creating a zoom sequence I get distorted images, see below. I don't get this in the Kalles distribution 2.11.1.
This makes it into the movie too when assembled.

Ouch, this looks like the "animate zoom" is saved as image instead of the final rendered image - possible timing race condition in the zoom renderer?  Does it still happen if you disable the zoom animation in the GUI?  Does the movie assembler use the image or the .kfb map files?  If it uses the map files then I have no idea what is going on, as the "animate zoom" is purely bitmap based afaik.  What was your window size and image size when rendering?  What was your zoom step size?

Ouch, this looks like the "animate zoom" is saved as image instead of the final rendered image - possible timing race condition in the zoom renderer?  Does it still happen if you disable the zoom animation in the GUI?  Does the movie assembler use the image or the .kfb map files?  If it uses the map files then I have no idea what is going on, as the "animate zoom" is purely bitmap based afaik.  What was your window size and image size when rendering?  What was your zoom step size?

Turning off "animate zoom" makes no difference. The kfb files (used by movie maker) are bad and have grid artifacts (see attached example rendered independently). Zoom step size = 1.24 (recommended by Kalle to eliminate zoom rectangle in animation, problem disappears at normal zoom step size 2), 640X360/ 2560X1440. Sample KFB file: https://www.dropbox.com/s/c9vu303r1xn6ndn/00029_6.10e076.kfb?dl=0

I reported this problem (grid artifacts) a while ago on the old forum where I (apparently wrongly) blamed Kalle's movie maker, see his reply there (I have only a few posts there). Movie: https://www.dropbox.com/s/5ydssdtxxowascu/k44_x264.m4v?dl=0

Zoom step size = 1.24 (recommended by Kalle to eliminate zoom rectangle in animation, problem disappears at normal zoom step size 2)

Ok, looking at the code, when rendering zoom out sequences it sets bReuseCenter, which does nearest-neighbour interpolation on the existing iteration data to generate the middle rectangle of the next frame's iteration data.  This leads to grid artifacts when the zoom size is not an integer, especially when it is applied again and again for subsequent frames.  Disabling bReuseCenter would render the whole frame each time and eliminate the artifacts, but increase rendering time (with zoom size 2 it would be 25% extra, possibly more in practice as the center usually has a higher iteration count).  I don't think there is a way to disable bReuseCenter from the GUI, I'll add that feature to my TODO list.

Here's the bReuseCenter code:
https://code.mathr.co.uk/kalles-fraktaler-2/blob/657afe29ae0a36a58b23e442dc38b978de5b6680:/fraktal_sft/fraktal_sft.cpp#l2945

Visible rectangles-in-rectangles is a MovieMaker bug as I understand it.  One way to write a MovieMaker that doesn't suffer from it is to crop the viewport to the central region when interpolating between neighbouring keyframes.  This has the cost of rendering eg 2160p keyframes for a 1080p video, before any supersampling for antialiasing.  Quite a high cost...

When creating a zoom sequence I get distorted images, see below. I don't get this in the Kalles distribution 2.11.1.

I now think this is a combination of series approximation overskipping, together with bReuseCenter (and I guess you have a zoom size close to 1).  See description of glitch type 1 here http://www.chillheimer.de/kallesfraktaler/tutorial.htm There was a similar report on the old forum recently.

I don't think there is a way to disable bReuseCenter from the GUI, I'll add that feature to my TODO list.

In case it helps: According to
http://www.fractalforums.com/kalles-fraktaler/kalles-fraktaler-2-9-2-and-key-frame-movie-maker-1-32/msg87212/#msg87212
bReuseCenter=0 if zoom stepsize <1.25 in that version (if I understood correctly).

zoom step = 1.24 has no problem in Kalle's latest 64.exe.