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Author Topic: Inflection mappings Celtic  (Read 799 times)
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Kalles Fraktaler
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« on: January 30, 2017, 03:25:42 PM »

Inflection mappings Celtic



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=20002

Applying Inflection points on a basic Celtic Julia shape
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Dinkydau
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« Reply #1 on: January 31, 2017, 02:27:31 PM »

Awesome

Does this exist in the celtic mandelbrot?
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TheRedshiftRider
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« Reply #2 on: January 31, 2017, 04:25:19 PM »

Beautiful.

Awesome

Does this exist in the celtic mandelbrot?
Would it? If it is like the standard inflection (following the rules of the standard m-set). It probably would not exist in the celtic because of the way inflection works in that fractal. I think.

Nevertheless it would be a nice feature.
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Kalles Fraktaler
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« Reply #3 on: January 31, 2017, 10:48:37 PM »

Beautiful.
Would it? If it is like the standard inflection (following the rules of the standard m-set). It probably would not exist in the celtic because of the way inflection works in that fractal. I think.

Nevertheless it would be a nice feature.
Sorry, this kind of inflection function includes sin, cos and tan, which I don't want to implement in high precision since they in turn requires Taylor series, i.e. iterations, to approximate the value in high precision.
Also I don't think the Series Approximation would work with this, since the pixels are from at least 3 different magnitudes.

So I am currently playing with double datatype only, and since this function already exists in UF I assume it is better in that program since I don't have an easy accessible UI in the program I made for myself.

And yes, this pattern is not possible in the Celtic fractal, since the pattern double itself differently. So this is a totally unnatural fractal smiley
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TheRedshiftRider
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« Reply #4 on: February 01, 2017, 06:55:40 AM »

Sorry, this kind of inflection function includes sin, cos and tan, which I don't want to implement in high precision since they in turn requires Taylor series, i.e. iterations, to approximate the value in high precision.
Also I don't think the Series Approximation would work with this, since the pixels are from at least 3 different magnitudes.

So I am currently playing with double datatype only, and since this function already exists in UF I assume it is better in that program since I don't have an easy accessible UI in the program I made for myself.

And yes, this pattern is not possible in the Celtic fractal, since the pattern double itself differently. So this is a totally unnatural fractal smiley
Oh.. I think I could have formulated that differently. I think this is really nice. Even though the pattern does not technically exist.
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youhn
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« Reply #5 on: February 01, 2017, 06:24:36 PM »

LOL.
What fractal (in the mathematical sense) is real anyway? Are we on that point that we consider the simple well known fractals (Mandelbrot, Burning Ship, etc) as REAL, while shapes and patterns created in other fashions are FAKE?  :hmh:When the word fractal came to be, it was more in the spirit of roughness and nature. The shape of trees, lungs, coast lines, mountain silhouettes, etc. As opposed to the well know orderly and infinite math shapes, these real world fractal are less orderly and only "fractal" on some order of scales of magnitude. When you zoom into or out from reality, the fractal dimension will at some point change.

However these inflection shapes are generated (I do not really understand at the moment) I have to say it looks beautiful! Are they easier or faster to compute when compared to the time-consuming process of morphing julias by zooming into them? How much flexibility does this method give?

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Kalles Fraktaler
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« Reply #6 on: February 01, 2017, 09:31:04 PM »

LOL.
What fractal (in the mathematical sense) is real anyway? Are we on that point that we consider the simple well known fractals (Mandelbrot, Burning Ship, etc) as REAL, while shapes and patterns created in other fashions are FAKE?  :hmh:When the word fractal came to be, it was more in the spirit of roughness and nature. The shape of trees, lungs, coast lines, mountain silhouettes, etc. As opposed to the well know orderly and infinite math shapes, these real world fractal are less orderly and only "fractal" on some order of scales of magnitude. When you zoom into or out from reality, the fractal dimension will at some point change.
In my perception the Mandelbrot fractal is a real thing.
For me one of the most fascinating things with the Mandelbrot set is that the formula is so simple, and that you discover patterns that were already there forever.
It is easy to imagine that an intelligent spieces at some other place and time in the universe also have computers that can render the Mandelbrot set and find the same locations as we do.

However these inflection shapes are generated (I do not really understand at the moment) I have to say it looks beautiful! Are they easier or faster to compute when compared to the time-consuming process of morphing julias by zooming into them? How much flexibility does this method give?
I described the mapping method I use here: http://www.fractalforums.com/images-showcase-(rate-my-fractal)/inflection-mappings/
With the exception that the outer dense pattern is not there, it is very similar to zoom-morphing, I have made comparisons and there is no remarable difference.
See the attachment, the top view has 4 inflection points, the bottom image is zoomed to 1.7e50.
It gives the same flexibility or even more, since you can add the inflection points anywhere, even in empty areas.
I can easily add say 15 inflection points in some minutes and render a 7680x4320 image in seconds, compared to do the same in KF which would take a week or probably two, which would be equivalent to zooming into some 1e4000.
Adding another 15 inflection points would take another some minutes, and is indeed impossible in KF since it would require zooming to some e1,900,000

The only difficulty is to make the images as nice as Dinkydau's and Fractal universe images, since because the pattern is also magnified around the inflection point, the outmost pattern get invisible small. So this Celtic image use only some 10 inflection points.


* compare.jpg (245.73 KB, 632x720 - viewed 115 times.)
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Kalles Fraktaler
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« Reply #7 on: February 01, 2017, 09:34:16 PM »

-
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