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cKleinhuis
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« on: April 12, 2011, 09:14:09 AM » |
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divide and conquer - iterate and rule - chaos is No random!
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bib
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« Reply #1 on: April 12, 2011, 09:25:43 AM » |
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Sam (aka s31415 here on FF) is a great artist and fractal programmer, I was lucky to have lunch with him last week  |
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Between order and disorder reigns a delicious moment. (Paul Valéry)
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Fractal Ken
Fractal Lover
Posts: 246
Proud to be 2D
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« Reply #3 on: April 12, 2011, 05:26:50 PM » |
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I will be waiting for more details of it!
Algorithmic worlds is my favorite fractal art blog. I believe the algorithm behind the Fractal expressionism post is Ducks. I've created one work using this method: I Don't See Any Ducks |
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Fortran will rise again
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Syntopia
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« Reply #4 on: April 12, 2011, 06:39:00 PM » |
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Yes, it looks like 'Ducks' - which is one of the most promising 2D fractals, I've seen. Version 0.8 of Fragmentarium contains an implementation, if you want to try it (and have a GLSL-capable GPU). The attached picture shows an example showing both the Julia and Mandelbrot type of the fractal. |
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Kali
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« Reply #5 on: April 12, 2011, 09:28:38 PM » |
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Good! another toy to play with  I love the patterns that generates. They are also good for mandala-like images... I just made this in Ultrafractal, applying ^4 to the plane for radial symmetry and then used a Julia version of the formula with my "checkerboard" coloring method.  Now I'll try to combine it with other formulas like Mandelbrot on real numbers and 2D Mandelbox, I think it will fit well with them  Thanks for the info! |
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s31415
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« Reply #8 on: April 13, 2011, 05:38:16 PM » |
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Yes, it looks like it is. These patterns appear when you iterate a "mirror transformation" combined with a conformal transformation. By "mirror transformation", I mean the transformation taking a half-plane or space and copying its mirrored version on the other half-plane/space. In particular, direct 3d analogs of these patterns are created by the so-called "Kaleidoscopic IFS" algorithm, that works exactly on this principle.
I don't quite know what is the Mandelbox algorithm, but I would guess it involve the type of mirror transformation mentionned above.
Sam
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bib
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« Reply #9 on: April 13, 2011, 05:41:25 PM » |
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Absolutely, the Mandelbox algorithm involves a "folding" which is what you describe as a mirror transfomation. You should look at this algorithm, I'm sure you'd love it, and our common friend prokofiev could explain it perfectly to you  |
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« Last Edit: April 13, 2011, 05:43:36 PM by bib »
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Between order and disorder reigns a delicious moment. (Paul Valéry)
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s31415
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« Reply #10 on: April 13, 2011, 05:43:55 PM » |
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Ah, yes, folding is a much better word. So yes, Ducks also works with folding.
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Kali
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« Reply #11 on: April 13, 2011, 05:46:01 PM » |
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What about a 3D version of Ducks?
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bib
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« Reply #12 on: April 13, 2011, 05:48:11 PM » |
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What about a 3D version of Ducks?
LUCAAAAAA ?? (let's ask Darkbeam ) |
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Between order and disorder reigns a delicious moment. (Paul Valéry)
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s31415
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« Reply #13 on: April 13, 2011, 06:43:56 PM » |
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Well, Kaleidoscopic IFS is a 3d version of this algorithm, in some sense. I don't think it is possible to generalize it much in 3d, because (always the same problem) the conformal group is small in dimensions larger than 2. For instance there is no conformal analog in 3 dimensions of the logarithm function used in Ducks.
Sam
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Kali
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« Reply #14 on: April 13, 2011, 07:13:06 PM » |
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Indeed... but I will try to do an orthogonal linear combination of two 2D planes (for Mandelbulb3D users, the same thing KaliLinComb formula does with Mandelbrot). It's not really a literal 3D version of it, but I think the results should be good. I'll give it a try using Trafassel's Gestaltlupe.
Also, I'd love to have your formula included into the fractal software I'm just writing (off course you'll be credited).
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