### (Question) Perturbation Code for Cubic and Higher Order Polynomials

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• Posts: 87

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #30 on: May 07, 2019, 01:37:34 PM »
Hi Claude,

I don't really think the type of glitch is so important. I see 3 possibilities...

1. Escape.
2. Iteration count = max iterations
3. Local maximum iterations reached for the reference pixel is less than max iterations set by the user. This is then marked as "Glitch".

So as I check for that we have a glitch, I compare with previous glitches and if |Z+z| < than the previously stored version, then this pixel becomes the best contender for the next reference. We do a full check of all "glitch" pixels and continue the process until we find a magic pixel where local max iteration = user set max iterations. Then we can calculate the iteration count for all the remaining pixels. This seems like a simple and efficient way to process all glitch pixels.

Does this make sense?
Paul the LionHeart

#### quaz0r

• Fractal Friar
• Posts: 117

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #31 on: May 07, 2019, 11:19:59 PM »
when we speak of perturbation glitches we arent referring to a maxiter fail or a prematurely-escaping reference.  if your reference iteration escapes early that is a condition which is easily identified.  in the context of perturbation iterations, by "glitch" we are referring to less-easily identified conditions where the utilization of limited-precision floating-point types within the iteration of the perturbation formula causes a catastrophic loss of precision which then results in that point being incorrectly solved.  often how this manifests is large areas whose points all seem to escape at the same iteration which then looks like large flat areas of the same color in the resulting image, instead of the structures and details that should be there if those points were solved correctly.  you'll become much more familiar with this once you get a more properly functional perturbation implementation going and start exploring deeper and more complex locations..

• Posts: 87

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #32 on: May 07, 2019, 11:36:20 PM »
Thanks Quazor,

Shucks, and here I was very proud of myself with an "almost" working version of perturbation. So the problem then becomes, what is the algorithm for detecting this kind of glitch? I'm sure that if we can choose a pixel inside that area, it will mean that the delta is small enough so precision isn't an issue. I run MPFR at a precision way beyond what is probably enough decimals, but the issue is more the delta that runs in floating point. So if the reference pixel is inside the glitch area, surely the delta would be so small that the precision is sufficient. Is this correct?

But then we still have the issue of detection of this kind of glitch.

Perturbation theory is fractal in nature, there's always more to learn LOL.

• 3f
• Posts: 1347

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #33 on: May 08, 2019, 12:53:01 AM »
here's an example of a glitch, and a corrected version of the same location, look closely

• Posts: 87

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #34 on: May 08, 2019, 01:06:57 AM »
Thanks Claude,

How does one detect this kind of glitch? Is my theory correct that if we find a pixel in the middle of a glitch and set it to reference, then the delta will be small enough so ordinary double float precision will handle it? This still leaves the issue of detection.

Any clues?

Thanks a million.

• Posts: 87

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #35 on: May 08, 2019, 10:17:07 PM »
Hi Claude and Quazor,

Are you able to guide me about dealing with the precision based glitches? How does one detect them and what can one do about it? Claude, you showed me the effect in your images. Do you have a location I can use as a test bed for these glitches?

Many thanks.

#### quaz0r

• Fractal Friar
• Posts: 117

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #36 on: May 08, 2019, 11:53:12 PM »
go ahead and get yourself a fistful of locations which produce large obvious glitch areas to test against so you can measure your progress.  go back and reread this thread (and many other long detailed threads on this forum and the old forum) for information on glitch detection.  for instance even within this thread claude already mentioned paul's glitch detection condition which you could easily add to your program and start experimenting with.

• Posts: 87

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #37 on: May 09, 2019, 12:24:57 AM »
Thanks Quazor,

I'll see what I can come up with. I'll read Pauldebrot's contribution again and see how I can implement it. I found it a little bit difficult to understand.

• Posts: 87

#### Re: Perturbation Code for Cubic and Higher Order Polynomials

« Reply #38 on: May 16, 2019, 01:57:04 PM »
Hi Friends,

I just want to extend a huge thanks to all who helped me build my Perturbation program.

Special thanks to Claude who really explained many things very well. I finally got glitch removal working.

With Glitches:

Without Glitches:

I was able to get a 15% improvement in speed using Horner's Rule as Claude suggested. I am able to get up to Z^28 without overflow of the Pascal coefficients.

Thanks also to Marcm200 and Quazor for your suggestions.

So my next challenge is abs() functions such as burning ship.

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