Another possible way to accelerate MB set deep zooming

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Offline knighty

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« Reply #165 on: August 04, 2018, 06:03:40 PM »
Cool!
Could you provide a Windows executable if such thing is possible? I don't have Haskell...
Those kind of glitches are probably caused by inaccurate escape radius estimation. Try using higher "orderM" or reduce the escape radius by some factor. For now the escape radius estimate is not very good. It needs some research. There are two questions to answer in order to get a better escape radius:
- how close is the bi-polynomial to a quadratic function ? There is a region around z=0 where the bi-polynomial is quadratic-like. How big is that region?
- how good is the bi-polynomial at approximating f(on)(z,c) ? Or how big is the region where the approximation error smaller than a tolerance?
Another question is about the dependency of the escape radius on the c parameter...

Maybe an adaptive maxiters could be a neat trick, base it on the period of the first minibrot (ordered from deep to shallow) whose superbailout we are within ?  Don't know what the best scaling formula would be.  Did you share your latest code?

EDIT: simpler just to use si < 1000 = maxsi and set maxiters = period * maxsi, seems to work in one test
That's a good method IMHO.

The code I'm working on have become a real mess. I don't think is would be helpful. Moreover, the comments may be misleading. I haven't found a good way to solve the glitches issue. I'm pretty sure it is solvable using the "super PT". The question is how to determine the good approximating (bi-)polynomials sequence ?

Anyway, here it is.

Offline claude

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« Reply #166 on: August 06, 2018, 12:03:39 AM »
No windows executable(s), the code is structures as many independent programs orchestrated by a bash script.  Sorry.  Maybe that WSL or whatever it is will be more productive, it's all CLI stuff so should work fine.  Or try a traditional VM.

Offline gerrit

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« Reply #167 on: August 06, 2018, 03:19:01 AM »
PT glitch correction when based on non-escaping reference point (nuclei) usually requires higher period mini's than the first reference.
It's not the same, but maybe something similar prevents SSA2 (1=SSA + PT, 2 = SSA all the way) from working.

Offline gerrit

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« Reply #168 on: August 15, 2018, 05:23:42 AM »
Would it be possible to make some small adjustments to the last nanomb binary:
https://fractalforums.org/fractal-mathematics-and-new-theories/28/another-possible-way-to-accelerate-mb-set-deep-zooming/277/msg8132#msg8132

It works very well, but there is a problem with "long double" which is much slower than "floatexp".

The other problem is the kfb export which is not completely compatible with KF. My workflow is render with nanamb then postprocess KFB in KF. When imported in KF you get all sorts of weird colors in the mini (interior DE).
I wrote a script to replace all negative entries in the KFB file with 0, but when importing to KF it still does not recognize interior points as interior points, but gives them some color. Workaround for me is to the replace that color with black in photoshop which works unless I'm unlucky and that color appears elsewhere.

An option not so save (negative) interior DE data would be good.

With those changes I think this is a great external rendering tool.

Offline claude

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« Reply #169 on: August 15, 2018, 10:29:21 PM »
I wrote a script to replace all negative entries in the KFB file with 0, but when importing to KF it still does not recognize interior points as interior points, but gives them some color.
I think you should replace negative DE like this:
the integer iteration count -> the maxiters value found in the KFB header (this signals the colouring to consider it as interior)
the floating point fraction iteration count -> 0 (anything other than -1 might work, -1 signals that it is a glitch)
the distance estimate (negative) -> absolute value of distance estimate (anything might work, it's not used for interior)

Offline gerrit

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« Reply #170 on: August 16, 2018, 12:36:07 AM »
Thanks. Just setting the integer count to maxiter suffices it seems.

Offline claude

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« Reply #171 on: February 17, 2019, 03:56:59 PM »
So I'm working on a bot to automatically deep zoom in various ways.  As a side effect, it gives me lots of deep locations to test NanoMB2 (as implemented in KF, which is mostly copy/pasta of knighty's code).

Good news:  simple straight zooms past many minibrots seems to work very well, maybe 3% of locations have issues.  See attached "rodney-selection-3.png".

Bad news: more interesting paths featuring elements such as zooms towards the principle Misiurewicz points of embedded Julia sets fail miserably (large flat featureless regions and hard line artifacts).  See attached "rodney-selection-5.png".

So far I'm testing with order 16, radius scale 0.1.  I'll try increasing the order (can't hurt I suppose) and fiddle with the scale (not sure whether it should be higher or lower in these cases...).

Offline gerrit

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« Reply #172 on: March 06, 2019, 04:27:57 AM »
I think this is a world record for highest magnification of a non-trivial location, a period \( 1660966 \) mini.
Zoom is \( 10^{2,000,000} \) at \( 10^{10} \) maximum iterations.
Location found using KallesFract NR zoom starting from -2 at zoom  \( 10^{1,000,000} \).
22 NR iterations on Intel i7-2600 3.5GHz took 2 months to find a mini.
Resulting location rendered at \( 10000^2 \) resolution using the compiled nanomb code posted here (https://fractalforums.org/fractal-mathematics-and-new-theories/28/another-possible-way-to-accelerate-mb-set-deep-zooming/277/msg8132#msg8132) took about 8 days on AMD Threadripper 2950X16 3.5 GHz.

I'll post the kfr file separately as it's too big to attach also.

Offline gerrit

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« Reply #173 on: March 06, 2019, 04:29:16 AM »
(Attachment belonging to previous post.)

Offline pauldelbrot

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« Reply #174 on: March 06, 2019, 06:59:56 AM »
Gerrit! I thought you'd been driven away for good when they fiddled with locking the image threads. Glad to see you're still around. You're one of the most innovative contributors around here.

And on the thread topic: is there a released, usable software that uses polynomial renormalization yet? Or still just pre-alpha experimental stuff?

Offline claude

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« Reply #175 on: March 06, 2019, 05:04:17 PM »
Gerrit! I thought you'd been driven away for good when they fiddled with locking the image threads. Glad to see you're still around. You're one of the most innovative contributors around here.
agree

Quote
And on the thread topic: is there a released, usable software that uses polynomial renormalization yet? Or still just pre-alpha experimental stuff?
Latest released KF has both nanomb1 (polynomial renormalization) and nanomb2 (chained multiple polynomial renormalization), though it's still experimental and has some issues:
0. sometimes output is bad, not a fully automatic foolproof rendering method yet
1. the series order can only be set by editing KFR in a text editor
2. the escape radius factor can only be set by editing KFR in a text editor
3. there is only 1 factor for all minibrots in the nanomb2 chain, which is probably suboptimal
4. they both use floatexp only, which is much slower than necessary for non-massively-deep locations

I plan to fix 1,2 and maybe 4 in the next release, but that won't be for a few months as I'm very busy at the moment.  help is very welcome, in particular for 4, if someone can do the maths for rescaled (long) double in the bivariate polynomial it would save me a lot of headaches (probably easier to do that with the standalone code in this thread, as kf is a lot harder to build)

Offline Dinkydau

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« Reply #176 on: March 06, 2019, 05:05:18 PM »
Very cool

Offline marcm200

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« Reply #177 on: March 10, 2019, 10:40:40 AM »
Astonishing! My first computer couldn't even store one of these 1000000 digit numbers.

With all these deep zooming, I got really interested in the automatic discovery process. Is there an introductory article or code documentation you could recommend reading?

Offline gerrit

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« Reply #178 on: March 12, 2019, 07:10:37 AM »
help is very welcome, in particular for 4, if someone can do the maths for rescaled (long) double in the bivariate polynomial it would save me a lot of headaches (probably easier to do that with the standalone code in this thread, as kf is a lot harder to build)
Math is pretty simple. Unscaled and with implied summation you have
\( f(z,c) = a_{ij}z^i c^j \)
whereas scaled (hatted variables) you have
\( f(z,c) = \hat{a}_{ij}\hat{z}^i \hat{c}^j \)
with \( \hat{z}=z/s \) and \( \hat{c} = c/r \).
s, r something like image size or pixel size.
So \( \hat{a}_{ij} = a_{ij}s^i r^j  \).
Just compute the hatted stuff instead.

double and long double works fine without scaling in the latest compiled nanomb posted here, it would just go a little further with scaled variables.


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