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Author Topic: Newton-Raphson zooming  (Read 3852 times)
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Dinkydau
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« on: December 23, 2016, 09:08:08 PM »

This must be the best breakthrough since perturbation! I just tested it a few times and it really works. It's simple and elegant. This makes zooming so much easier.

Around 2^1000 it starts to become much slower. I remember that being a depth where other things get slower as well. I would guess it's about as fast as manual zooming from there on, except you can do other things while kalles fraktaler is busy.
« Last Edit: December 24, 2016, 01:12:20 PM by Dinkydau » Logged

Kalles Fraktaler
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« Reply #1 on: December 28, 2016, 12:19:57 AM »

This must be the best breakthrough since perturbation! I just tested it a few times and it really works. It's simple and elegant. This makes zooming so much easier.

Around 2^1000 it starts to become much slower. I remember that being a depth where other things get slower as well. I would guess it's about as fast as manual zooming from there on, except you can do other things while kalles fraktaler is busy.
Yes it is indeed a huge breakthrough for me at least.
And I think it is much faster than manual zooming all the way down.
It took 2 months for me to reach e10000 the first time with manual and automatic zoom, but only some week to reach e20000 with NR... smiley
If you use zoom size 32, and zoom to e20000 manually, you would need +6600 clicks...

All thanks to the generously shared code by claude!
« Last Edit: December 28, 2016, 12:46:05 AM by Kalles Fraktaler, Reason: Rephrase » Logged

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Adam Majewski
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« Reply #2 on: December 28, 2016, 01:01:39 PM »

Where is more description / code ?
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claude
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« Reply #3 on: December 28, 2016, 04:03:29 PM »

Use box method to find the period (suggested to me by Robert Munafo), described here: http://www.mrob.com/pub/muency/period.html sample code here https://code.mathr.co.uk/mandelbrot-numerics/blob/HEAD:/c/lib/m_d_box_period.c

Using period, and initial guess in the current view, find the nucleus c where F^p(0,c)=0 using Newton's method.  sample code https://code.mathr.co.uk/mandelbrot-numerics/blob/HEAD:/c/lib/m_d_nucleus.c

Find the size estimate using formula from http://ibiblio.org/e-notes/MSet/windows.htm sample code https://code.mathr.co.uk/mandelbrot-numerics/blob/HEAD:/c/lib/m_d_size.c

Use size estimate s to choose a view radius r around the nucleus c.  Use (something like)  r = 4 s to view the minibrot, or r = 4 sqrt(s sqrt(s)) to view the final 2-fold embedded Julia set.  (Note: I'm not 100% sure on the formula for viewing the embedded Julia set, it seems to work for me most of the time, maybe Kalles Fraktaler uses a different formula?)
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Kalles Fraktaler
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« Reply #4 on: December 28, 2016, 10:36:14 PM »

I convert the zoom of the final minibrot to powers of 2.
Then multiply it with 3/4 and convert back to zoom.
It works well for most cases. Some times a few zoom-in or -out is needed, it is easy to determine by the density of the resulting view.
However when making short-cuts, as described by TheRedShifter, this doesn't work so well
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Adam Majewski
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« Reply #5 on: December 31, 2016, 02:04:10 PM »

i understand idea of perturbation method.
Why this method is better then perturbatiion ?
Can you describe it in simple words ?
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quaz0r
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« Reply #6 on: December 31, 2016, 03:34:34 PM »

it is not a different rendering method (they are still using perturbation).  it is automated zooming.  they use newton's method to find and progressively refine the precision of the location of the minibrot at the center of a pattern.  this allows them to arbitrarily select a magnification between the location they started at and the final minibrot they calculate to be at the center of that location.
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Dinkydau
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« Reply #7 on: January 02, 2017, 08:17:07 AM »

Thanks for the links, Claude. I was wondering how this worked and I couldn't find anything.
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Dinkydau
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« Reply #8 on: January 02, 2017, 08:43:14 AM »

Yes it is indeed a huge breakthrough for me at least.
And I think it is much faster than manual zooming all the way down.
It took 2 months for me to reach e10000 the first time with manual and automatic zoom, but only some week to reach e20000 with NR... smiley
If you use zoom size 32, and zoom to e20000 manually, you would need +6600 clicks...

All thanks to the generously shared code by claude!
It must help that your zooms to depths like E20000 were low on iterations. That makes the process of finding the period a lot shorter. I'm currently using it to zoom to E2538 and I can see this making faster progress than I could have by manual zooming in mandel machine (~ 2^6,3 magnification per click, very efficient reference point calculation). I estimate the period is roughly 87 million. Reference points would take close to an hour eventually. It's probably just right after the slowdown around 2^1000 that manual zooming can be faster.
« Last Edit: January 02, 2017, 08:49:23 AM by Dinkydau » Logged

Kalles Fraktaler
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« Reply #9 on: January 02, 2017, 02:08:01 PM »

It must help that your zooms to depths like E20000 were low on iterations. That makes the process of finding the period a lot shorter. I'm currently using it to zoom to E2538 and I can see this making faster progress than I could have by manual zooming in mandel machine (~ 2^6,3 magnification per click, very efficient reference point calculation). I estimate the period is roughly 87 million. Reference points would take close to an hour eventually. It's probably just right after the slowdown around 2^1000 that manual zooming can be faster.
Yes you are right, the amount of iterations and period number has a big impact on the speed of NR calculations, since every loop is iterating the iterations.
And every shape stacking is doubling the iterations/period, so the number increases quickly and exponential.
So the depth itself doesn't have much impact smiley
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Dinkydau
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« Reply #10 on: January 06, 2017, 10:40:39 AM »

A negative percentage
Let's hope this is not a bad sign.

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Kalles Fraktaler
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« Reply #11 on: February 16, 2017, 09:43:56 PM »

A negative percentage
Let's hope this is not a bad sign.

<Quoted Image Removed>
No it will work
100*progress/max
where 100*progress overflows maximum integer value of 2147483648
So you have a period of more than 21,474,836?  shocked

This occurs also when calculcating the reference if you have more than 21,474,836 iterations...
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Dinkydau
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« Reply #12 on: February 16, 2017, 11:39:37 PM »

That explains it. I've seen it happen a lot with the reference but no errors ever occurred because of it.

It's still not done because I assigned the process a low prority and I'm using the Newton-Raphson zooming very intensively. I've got 9 instances of Kalles Fraktaler open at the moment.
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