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Author Topic: Mandelbrot record ideas  (Read 773 times)
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youhn
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« on: February 04, 2017, 10:36:15 PM »

In reaction to the current active topics on records on zoom depth.

Since new calculation methods, zoom levels is not a direct indication of computing time. The effort goes into finding a minibrot location at deeper levels. This is true as long as we cannot predict the exact locations of minibrots (will a method arise?). So what is difficult in computing? Maybe think in amount of iterations instead of zoom depth. But that's also been dealt with somewhat.

Would there be a list or even some small collections of Mandelbrot location with the highest difference in required iterations? These location tend to break current methods of calculation, or at least throw in some obstacles.

Other views on possible records are welcome.
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Adam Majewski
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« Reply #1 on: February 05, 2017, 09:34:38 AM »

1. Related with Mandelbrot set are Julia sets.
There are NO images of Cremer Julia sets
https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/cremer


2. images of dense parts of Mandelbrot or Julia sets ( all pixels are boundary pixels = usually black) needs new approach. Maybe coloring branches of M set ?

http://mathoverflow.net/questions/187842/is-there-an-almost-dense-set-of-quadratic-polynomials-which-is-not-in-the-inte/254533#254533


3. Parabolic enrichment  

HTH
« Last Edit: February 06, 2017, 09:16:46 PM by Adam Majewski, Reason: spelling » Logged
Dinkydau
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« Reply #2 on: February 06, 2017, 09:11:11 PM »

Interesting ideas but those are all unreachable limits if I understand correctly.
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Kalles Fraktaler
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« Reply #3 on: February 06, 2017, 11:48:01 PM »

I had ideas of whether it is possible to render deep zoom Mandelbrot locations without zooming at all.
We are able to trasform basic shapes with inflection, but that only applies on that shape and not the surrounding pattern of the shape.
I wonder if it is possible at all, to transform the surrounding in the same way.
I hope you understand what I mean, http://www.fractalforums.com/index.php?topic=25294.msg99572#msg99572
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SamTiba
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« Reply #4 on: February 07, 2017, 12:22:40 AM »

I would like to find a proper information on your 'inflection'-method at all, as the built in function seems to vary from the use on your recent post pictures and my head is running like crazy to get those properties linked together, also the used formulas with the several inflection points.

Maybe I'm the only slowpoke here, but that would really bring us forward, maybe some others have interesting ideas like claude here?

It doesn't have to be a long essay, maybe in 5-10 sentences what it's about and how to use the basics?
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Dinkydau
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« Reply #5 on: February 07, 2017, 01:09:19 PM »

I had ideas of whether it is possible to render deep zoom Mandelbrot locations without zooming at all.
We are able to trasform basic shapes with inflection, but that only applies on that shape and not the surrounding pattern of the shape.
I wonder if it is possible at all, to transform the surrounding in the same way.
I hope you understand what I mean, http://www.fractalforums.com/index.php?topic=25294.msg99572#msg99572
If you succeed that would be amazing. I wouldn't know where to start but the whole structure is predictable. If only there was a simple formula that generates it instead of having to simulate it.

I would like to find a proper information on your 'inflection'-method at all, as the built in function seems to vary from the use on your recent post pictures and my head is running like crazy to get those properties linked together, also the used formulas with the several inflection points.

Maybe I'm the only slowpoke here, but that would really bring us forward, maybe some others have interesting ideas like claude here?

It doesn't have to be a long essay, maybe in 5-10 sentences what it's about and how to use the basics?
I thought this page has a good visulatisation: http://www.karlsims.com/julia.html
« Last Edit: February 07, 2017, 01:16:38 PM by Dinkydau » Logged

youhn
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Shapes only exists in our heads.


« Reply #6 on: February 07, 2017, 05:38:40 PM »

Interesting ideas but those are all unreachable limits if I understand correctly.

Yeah, this makes it wonderful to aim records at!  grin
(Zooming to the end of the Mandelbrot detail is also impossible)

Kalles, I'm not sure if I understand you correctly. You want to apply the inflection method, but instead of local (zoomed into a finite area) to the whole set (or at least larger surrounding set)? Wouldn't that defeat the whole point of doing inflection anyway? I mean, if you are going to apply it to the whole set with enough resolution, I think it would have the same "difficultness" compared to just zooming in and do the julia-morping the classic way.
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