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From: Greg M Johnson
Subject: Greg's mandels answering Warp on color differentiation vs. structure complexity
Date: 15 Nov 2000 13:30:57
Message: <3A12D505.1815CAD8@my-dejanews.com>
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I had claimed that (until you hit a wall with precision) a fractal like
a Mandelbrot or perhaps a Julia would have infinite complexity to its
structure as one zoomed to higher and higher levels.
I argued that the parameter following the word mandel in the pigment
term --the "max iterations" merely determined the number of color levels
the pattern was divided into, NOT the actual complexity of the
structure. Here is my proof.
Four images, all with exactly the same scene file. The only thing that
was changed was the iterations and the camera angle (effective zoom).
We have below
mandel 30 iterations camera angle 0.0002 //(200ppm)
mandel 30 iterations camera angle 0.02 //(20000ppm)
mandel 300 iterations camera angle 0.0002 //(200 ppm)
mandel 300 iterations camera angle 0.02 //(20000ppm)
The complexity of the structure doesn't change with changing the max
interations. One's ability to see **some** of the finer detail does,
however. He had confused these two concepts.
In Warp's Julia forest scene, the complexity of the structure
determines the fineness of his "trees" and the max iterations parameter
determines the number of demarcations in tree height.
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Attachments:
Download '30colors200ppm.jpg' (8 KB)
Download '30colors20000ppm.jpg' (8 KB)
Download '300colors200ppm.jpg' (11 KB)
Download '300colors20000ppm.jpg' (10 KB)
Preview of image '30colors200ppm.jpg'
Preview of image '30colors20000ppm.jpg'
Preview of image '300colors200ppm.jpg'
Preview of image '300colors20000ppm.jpg'
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This is the correct image for mandel 30, 0.0002 camera angle.
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Attachments:
Download '30colors200ppm.jpg' (7 KB)
Preview of image '30colors200ppm.jpg'
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Greg M. Johnson <gre### [at] my-dejanews com> wrote:
: This is the correct image for mandel 30, 0.0002 camera angle.
And proves my allegation (in the other thread) true :)
--
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
Post a reply to this message
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No. There is still structural complexity in "your" x-z plane, or fineness and
number of tree trunks,, but a great differentiation in the colors, or your
tree heights.
Warp wrote:
> Greg M. Johnson <gre### [at] my-dejanewscom> wrote:
> : This is the correct image for mandel 30, 0.0002 camera angle.
>
> And proves my allegation (in the other thread) true :)
>
> --
> main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
> ):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
Post a reply to this message
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Greg M. Johnson <gre### [at] my-dejanewscom> wrote:
: No.
What do you mean "no"? I see 8 colors in the image. The border of the
interior of the set (colored white in this case) is quite smooth and has
quite small amount of complexity. You could recreate it with a spline using
some tens of points. If you zoomed a bit more on the border of the set you'll
end up with a straight line.
Is that "infinite complexity" to you? A straight line is not "infinitely
complex" in my opinion.
To get infinite complexity you have to iterate an infinite number of
times. Only then you can zoom as big as you want and you will never get
straight lines nor smooth curves in the border of the set.
: There is still structural complexity in "your" x-z plane, or fineness and
: number of tree trunks,, but a great differentiation in the colors, or your
: tree heights.
Sorry, I didn't understand this.
--
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
Post a reply to this message
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