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Author Topic: Beyond the Cygnus Anomaly  (Read 446 times)
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Pauldelbrot
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pderbyshire2
« on: May 19, 2014, 12:03:50 AM »

Beyond the Cygnus Anomaly



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=16038

This is another Triple Matchmaker spacefilling Julia that looks like something in outer space. It's also another one from near to a Herman ring parameter value. The near-ring takes the form of the denser nebula regions, with two more Julias in the "outside" and "inside" regions -- one a dragonlike structure with starburst cores joined in triple spirals (noticeable especially at bottom center) and one consisting of seven-armed spirals (noticeable especially at top center).

A bit above center left, note a line of three seahorsey shapes in the nebula -- those are part of the almost-a-Herman-ring itself. So are the dark-cored shapes a bit below the image's exact center, and the double spiral at the image's center. The "pulsars" a bit above the left group of horses (and scattered elsewhere) and the other "stars" are preimages of infinity.

Or ignore all of this and just enjoy all the spirals and subtle gradations of color and translucency here. (Though, despite appearances of translucency, this whole thing was computed in one layer.)
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Dinkydau
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« Reply #1 on: May 19, 2014, 12:56:00 AM »

exceptional
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Chillheimer
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Just another fractal being floating by..


chilli.chillheimer chillheimer
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« Reply #2 on: May 19, 2014, 08:58:31 AM »

hey paul!
I really love your pictures, they are very special! they're actually the only picture-threads that I know I have to click..

But I have to admit, I don't have the slightest idea what you are talking about in your descriptions.. wink
triple-matchmaker, herman ring parameter...
do you approach your art in a scientific way?
how long have you been doing these pictures?

and I think I read this somewhere before, but can't find it anymore: what program do you use? are these raw fractals, or is there post-editing happening?
I'd love so much to see zoom-movies with that kind of quality...
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--- Fractals - add some Chaos to your life and put the world in order. ---
Pauldelbrot
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Posts: 2592



pderbyshire2
« Reply #3 on: May 20, 2014, 02:03:28 AM »

exceptional

Thanks!

hey paul!
I really love your pictures, they are very special! they're actually the only picture-threads that I know I have to click..

Wow, thanks!

Quote
But I have to admit, I don't have the slightest idea what you are talking about in your descriptions.. wink
triple-matchmaker, herman ring parameter...
do you approach your art in a scientific way?

I know much of the underlying mathematics, and exploit that knowledge to discover interesting fractals and ways of coloring them.

Triple Matchmaker is a fractal-producing system I discovered a year or two ago:

z_{n+1} = \frac{z_n + \frac{a}{\sqrt{3}}}{b(z_n^3 - \sqrt{3}az_n^2 + cz_n + \frac{ac}{\sqrt{3}})} + d

The critical points are at -a, 0, and a, with another critical value at d.

A Herman ring parameter is a parameter value (in the case of Triple Matchmaker, a combination of a,b,c,d) that produces a type of attractor known as a Herman ring. The Julia sets for parameters that are almost, but not quite Herman ring parameters can be exceptionally beautiful with convoluted rings of dense structures wrapped around other shapes. (At the actual Herman ring parameter value, these solidify into a hollow variant of a simple filled-in Julia set such as the Golden Mean Julia fractal.)

Quote
how long have you been doing these pictures?

Oh, around three decades, on and off. Two with internet access and the ability to publish things to others.

Quote
and I think I read this somewhere before, but can't find it anymore: what program do you use?

A few different ones, including custom-written stuff.

Quote
are these raw fractals, or is there post-editing happening?

Generally directly rendered, without postwork of the "makes it no longer pure" sort. Sometimes I do use external image editors to downsample, or assemble and then downsample after rendering in pieces, or similar, to have more control over antialiasing and divide bigger jobs into pieces.

Quote
I'd love so much to see zoom-movies with that kind of quality...

Talk to Congress and the FCC about getting real broadband competition so we can all have cheap 100Gbit fiber to the door in North America like they do in South Korea. Then it might be possible for Youtube to stream really good quality (non-blockying-up) streams in HD without buffering pauses...and for people to upload multi-gigabyte video files without it taking ages and then getting screwed on overage fees by their friendly neighborhgood telco/cableco duopoly. smiley
« Last Edit: May 20, 2014, 02:06:13 AM by Pauldelbrot » Logged

reactorman
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« Reply #4 on: May 20, 2014, 07:10:23 PM »

A Herman ring parameter is a parameter value (in the case of Triple Matchmaker, a combination of a,b,c,d) that produces a type of attractor known as a Herman ring. The Julia sets for parameters that are almost, but not quite Herman ring parameters can be exceptionally beautiful with convoluted rings of dense structures wrapped around other shapes. (At the actual Herman ring parameter value, these solidify into a hollow variant of a simple filled-in Julia set such as the Golden Mean Julia fractal.)

And all this time I thought it was like a "Where's Waldo?" thing.  I was looking for Herman Munster hiding all this time!   tease

Jim  -  reactorman
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