### Another possible way to accelerate MB set deep zooming

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• 3f
• Posts: 1897

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #195 on: November 24, 2019, 08:11:10 PM »
NanoMB2 also generates an image with artifacts. Does it happen to me alone, or has anyone discovered this?
I've used nanomb2 quite a bit and never saw that particular effect.

• 3f
• Posts: 1897

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #196 on: November 25, 2019, 02:52:21 AM »
It precisely.

Claude, will not be able to advise for what reason these artifacts arise, which resulted from the rendering of this fractal in Nano MB?

Code: [Select]
nanomb.exe --kfr test_x1.kfr --period 2449 --width 500 --height 500 --orderM 4 --orderN 4 --output_ppm s.ppm --force_type floatexp
Period is 2489, not 2449.

#### vasyan

• Strange Attractor
• Posts: 84

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #197 on: November 25, 2019, 06:07:08 AM »
Period is 2489, not 2449.

However, a red rectangle is drawn for the period as 2489.  :(

• 3f
• Posts: 1897

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #198 on: November 25, 2019, 07:15:26 AM »
I get attached from compiled nanomb64_i7.exe posted here a while ago.
The other method (recursing through parents) does not really work in a reliable way, maybe you used that (I think Claude called that NMB2).
BTW no need for floatexp, just double is enough.
Code: [Select]
 time ./nanomb64_i7.exe --kfr ./test_x1.kfr --maxiters 250000 --period 2489  --width 500 --height 500 --orderM 4 --orderN 4 --output_ppm s.ppm --output_kfb s.kfb --force_type 'floatexp'
Erroring the period as 2449 give second attachment.

• 3f
• Posts: 1897

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #199 on: November 27, 2019, 04:05:37 AM »
BTW here's the 2489 mini, rendered using NanoMB1 from Kalles Fractaler.

#### vasyan

• Strange Attractor
• Posts: 84

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #200 on: November 27, 2019, 04:55:41 AM »
Period is 2489, not 2449.
How is it possible to calculate the true period?
Are there any calculation criteria, or is this a random number?

• 3f
• Posts: 1897

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #201 on: November 27, 2019, 08:05:53 AM »
How is it possible to calculate the true period?
Are there any calculation criteria, or is this a random number?
Maybe it's random in that if you give me a (very small) square containing a section of the M-set boundary then the infinite set of all periods of all minis in that square has random integers in it. Or maybe there is a predictable pattern. Complicated way of saying don't know I guess.

• 3f
• Posts: 1319

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #202 on: November 27, 2019, 01:28:40 PM »
How is it possible to calculate the true period?
Robert Munafo's polygon iteration method.  Search Mu-Ency.
Knighty's Taylor ball iteration method.  Search this forum,

Both find the lowest period nucleus in a region.  If there is no nucleus in the region (either 100% exterior, or 100% interior not surrounding a nucleus) then I don't know what happens.

The polygon method can be adapted to pre-periodic Misiurewicz points.  Probably the Taylor ball method can be too.
A version of the ball method can be adapted to Burning Ship etc using Jacobians, where the polygon method can sometimes fail due to early folds.

#### vasyan

• Strange Attractor
• Posts: 84

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #203 on: November 27, 2019, 04:37:15 PM »
Robert Munafo's polygon iteration method.  Search Mu-Ency.
Knighty's Taylor ball iteration method.  Search this forum,

Both find the lowest period nucleus in a region.  If there is no nucleus in the region (either 100% exterior, or 100% interior not surrounding a nucleus) then I don't know what happens.

The polygon method can be adapted to pre-periodic Misiurewicz points.  Probably the Taylor ball method can be too.
A version of the ball method can be adapted to Burning Ship etc using Jacobians, where the polygon method can sometimes fail due to early folds.

As I understand it, it is impossible to calculate the period value using a simple method? Something like the function Period = FindPeriod ();
In this case, how can an ordinary user who is not sophisticated with higher mathematics be able to specify period values?

• 3f
• Posts: 1319

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #204 on: November 27, 2019, 04:52:01 PM »
In this case, how can an ordinary user who is not sophisticated with higher mathematics be able to specify period values?

Use the implementations in KF. From the manual:

Quote
It is required to set the period in the Location dialog before
enabling NanoMB1. Using Newton zoom sets the period automatically.

It is recommended to enable Reuse Reference after recalculating with
NanoMB1.  A new reference is calculated automatically after each Newton
zooming, whatever the setting of Reuse Reference.

Quote
It is recommended to set the period limit in the Location dialog before
enabling NanoMB2, otherwise it uses the maximum iteration count which
may take significantly longer.  Using Newton zoom sets the period limit
automatically.

It is recommended to enable Reuse Reference after recalculating with
NanoMB2.  A new reference is calculated automatically after each Newton
zooming, whatever the setting of Reuse Reference.

Otherwise there is also my mandelbrot-numerics library for command-line algorithms, and I'm working slowly on making it accessible in a web browser.

#### vasyan

• Strange Attractor
• Posts: 84

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #205 on: November 28, 2019, 03:14:50 PM »
Use the implementations in KF. From the manual:

Thanks, Claude
However, I had to spend time to get the right result. In my opinion, the user interface is not very well organized, it would be desirable to calculate the period value with just one click on the button near the period input field.

#### vasyan

• Strange Attractor
• Posts: 84

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #206 on: November 30, 2019, 10:14:24 AM »
I don't understand why it wouldn't work when the center doesn't escape. In the case you gave, the "good" period is 155. The higher periods are all multiples of 155 because they correspond to the discs. In SSA context, the escape radius of the cardioid is much bigger than those of the discs.
I hope, this will be solved in nanomb02 soon enought.

Here is a new version of nanomb where I tried to solve the 'dirty spots' issue. They are definitely caused by the interior DE code: When the root finding loop ends, some points may be erroneously classified as inside.
By the way, the source code (nmb02_00.cpp for example) during compilation works differently
than the exe file that comes in the same archive.
For example, in the nanomb-2018-07-12 archive.zip attached to this post.
And that there are two versions of nanomb64_generic.exe and nanomb64_i7.exe?
There is no explanation in the archive, but I am not a telepath to learn more about them.
The app nanomb64_i7.exe I have no letters on the screen, but just stops working after the launch. Where is the source code nanomb64_i7?

---------------------------------------------------------------
Something I could do without using third-party software.

#### knighty

• Fractal Feline
• Posts: 195

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #207 on: November 30, 2019, 03:56:33 PM »
The only difference is that nanomb64_i7.exe was compiled for i7 CPU. All executables are provided for those who can't or don't want to compile the source code.

All the programs that I posted here are experimental. They are not user friendly at all.

#### vasyan

• Strange Attractor
• Posts: 84

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #208 on: November 30, 2019, 05:14:42 PM »
The only difference is that nanomb64_i7.exe was compiled for i7 CPU. All executables are provided for those who can't or don't want to compile the source code.
I approximately understood that, however, if the program is launched in an environment not intended for its operation, it would be appropriate to display an error message.

All the programs that I posted here are experimental. They are not user friendly at all.
The main thing is that it works and produces the correct result!
And convenience is not particularly important, at least for experiments.

#### vasyan

• Strange Attractor
• Posts: 84

#### Re: Another possible way to accelerate MB set deep zooming

« Reply #209 on: December 01, 2019, 03:09:43 PM »
All executables are provided for those who can't or don't want to compile the source code.
However, I managed to get the program to run without errors. The fact is that I compiled your code in Visual Studio, and at first the program crashed, the problem was solved by increasing the size of the stack to 2,000,000 (in the project properties). And also I replaced
Code: [Select]
typedef long double R_lo; on
Code: [Select]
typedef floatexp R_lo;At the same time, it became possible to render with zoom more e+300.

Compared the program run time in two versions:

1. With R_lo = long double:

total time: ‭3008.39
pre computations time: 4.73405
rendering time: 3003.66

2. With R_lo = floatexp:
total time: 1283.12
pre computations time: 832.164
rendering time: 450.959

So the floatexp option turned out to be faster
« Last Edit: December 01, 2019, 03:33:16 PM by vasyan »

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