Title: Fractal expressionism Post by: cKleinhuis on April 12, 2011, 09:14:09 AM just found on orbittrap.ca a nice new algorithm:
http://www.algorithmic-worlds.net/blog/blog.php?Post=20110217 :) Title: Re: Fractal expressionism Post by: bib on April 12, 2011, 09:25:43 AM Sam (aka s31415 here on FF) is a great artist and fractal programmer, I was lucky to have lunch with him last week :)
Title: Re: Fractal expressionism Post by: Kali on April 12, 2011, 04:15:22 PM I will be waiting for more details of it!
BTW, Is really easy to find face-like shapes in bilateral symmetric images, I use to play with that, like here: http://www.fractalforums.com/index.php?action=gallery;sa=view;id=6630 http://www.fractalforums.com/index.php?action=gallery;sa=view;id=6607 Title: Re: Fractal expressionism Post by: Fractal Ken on April 12, 2011, 05:26:50 PM 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 (http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227). I've created one work using this method: I Don't See Any Ducks (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=5949) Title: Re: Fractal expressionism Post by: Syntopia on April 12, 2011, 06:39:00 PM Yes, it looks like 'Ducks' - which is one of the most promising 2D fractals, I've seen.
Version 0.8 of Fragmentarium (http://syntopia.github.com/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. Title: Re: Fractal expressionism Post by: Kali on April 12, 2011, 09:28:38 PM Good! another toy to play with ;D
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. (http://img59.imageshack.us/img59/9284/duckmandala.jpg) 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 :D Thanks for the info! Title: Re: Fractal expressionism Post by: s31415 on April 13, 2011, 04:38:41 PM Hi,
Yes, as Fractal Ken mentionned, it is created with the "Ducks" formula. You can learn more about it here: http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227 and here: http://www.algorithmic-worlds.net/blog/blog.php?Post=20110319 Actually, I announced it on Fractal Forums a while ago in "Theory and research": http://www.fractalforums.com/new-theories-and-research/ducky-thalis-and-co/ In addition to Syntopia's implementation in Fragmentarium, I recently released a public version of the algorithm for UltraFractal. Look for the Ducks formula in sam.ufm (but update your formulas first...). Best, Sam Title: Re: Fractal expressionism Post by: bib on April 13, 2011, 05:01:57 PM Look at the texture in this rotated Mandelbox. Is that a Ducks pattern or something much more basic?
(http://nocache-nocookies.digitalgott.com/gallery/4/492_19_12_10_9_11_58.jpeg) http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4806 Title: Re: Fractal expressionism Post by: s31415 on April 13, 2011, 05:38:16 PM 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 Title: Re: Fractal expressionism Post by: bib on April 13, 2011, 05:41:25 PM 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 ;)
Title: Re: Fractal expressionism Post by: s31415 on April 13, 2011, 05:43:55 PM Ah, yes, folding is a much better word. So yes, Ducks also works with folding.
Title: Re: Fractal expressionism Post by: Kali on April 13, 2011, 05:46:01 PM What about a 3D version of Ducks?
Title: Re: Fractal expressionism Post by: bib on April 13, 2011, 05:48:11 PM What about a 3D version of Ducks? LUCAAAAAA ?? (let's ask Darkbeam ;)) Title: Re: Fractal expressionism Post by: s31415 on April 13, 2011, 06:43:56 PM 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 Title: Re: Fractal expressionism Post by: Kali on April 13, 2011, 07:13:06 PM 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). Title: Re: Fractal expressionism Post by: s31415 on April 13, 2011, 07:32:12 PM Sure, I guess when an algorithm is published it's public domain.
Title: Re: Fractal expressionism Post by: DarkBeam on April 13, 2011, 07:32:37 PM What about a 3D version of Ducks? LUCAAAAAA ?? (let's ask Darkbeam ;)) Here it is; z = log(yabs(z)+C) Simply, go in reverse direction, so 1. abs of y 2. add c 3. log. I chosen log4D ^-^ Mandelbulb3Dv16{ N.....S....O/...s/...2....kV6zLcNdD4.XFfjPCTeb3Ej1o2R4lZswHRGBmbFQ7CzAbEEuDO2s.E ................................eD4A.EqbNz1........6./..................y.2..... ................/ME//....6............E2.....sB6MPaRzOsD/..........c./...w1/...U z.....kD..../2EsuFVf53imzcNaNaNaNayj.............................y1...sD...../.. .w1...sDnvtvYNrj4y1..........SK5ic7ZW8fjP07Utt/WSrvwSyCNqxfVzUTvRW7ZW8fjtrSbMGdc munNRsWaI8egykE55AaRzOsD......o3......................sD..kz0................... ..............................LRR4.0qpN.UOLb/UnRR4.orpN.cVLb/.ESR4.............. .....................wzzz1.U..6.P....M4...EB....W....61....F....8/...I1....UJl22 ...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0. FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c.. zzzz.................................2U.8.kzzzD................................. /6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq 40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3................................. E....A....E.....I....2....kL/7qQN/UPbxoMo/UQ.................................... ..........E91lluWPX4z0........zj................................................ ................................................................................ .....................2.....3....1....wJMYFqE.................................... ..............................zD........kz1........wz........................... ................................................................................ ................................/....E/.........TloPbF1F........................ ........................................U.2..................................... ................................................................................ ............................................} But of course it is 2D, because this formula is all inside! :) Have a nice day my friend ^-^ Title: Re: Fractal expressionism Post by: DarkBeam on April 13, 2011, 07:56:21 PM Using abs(z):
Mandelbulb3Dv16{ N.....S....O/...Y/...2....EuolfCpnPA.jMlV8KFEF2EdOqW8hNrIxPihl.EqQL8.lqUGw.VsZ0k ................................OaNaNaNadz1........A./..................y.2..... ................/ME//....6EM/.........E2.....QzIXLua2PrD/..........c./...wX....U z.EnAnQD..../2UaNaNaNaNmz...........BnAnAnAngz9..................y1...sD...../.. .wHnAnQDECayXi7lqx1..........UjJy0vma8ej.cmZCTyLOuX0n/DEQb/QzE3HlfH0N.rDUb4/84IM Ou1uyf2D7Y/QzGgfKy1rN.rD......o2......................sD..kz0................... ..............................LRR4.0qpN.UOLb/UnRR4.orpN.cVLb/.ESR4.............. .....................wzzz1.U..6.P....M4...EB....W....61....F....8/...I1....UJl22 ...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0. FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c.. zzzz.................................2U.8.kzzzD................................. /6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq 40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3................................. E....E..........I....2....kL/7qQN/UPbxoMo/UQ.................................... ..............................zj................................................ ................................................................................ .....................2.....3..../....wJEWBbK.sqNklKRn/.......................... .....................kTel9RHW/pD........kz1........wz.........zD................ ................................................................................ ................................/....E/...k.....T34NYB2......................... ........................................kz1........wz.........zD................ ................................................................................ ..........................................E.....I.........kLAxqNoE2............. ...................................................6./.......................... ................................................................................ ........................................................} :sleepy: Title: Re: Fractal expressionism Post by: Kali on April 19, 2011, 10:39:18 PM :D
(http://img215.imageshack.us/img215/8485/ducks3d.jpg) There are 2 cuts: x=0, y=0 (being z the height) I tried lots of differents methods to decide if a voxel is inside or outside, and many Julia constants. This is one of the best results. I'll post more later... also I want to go inside that cracks but the software (Gestaltlupe) is not so easy to handle, and is a bit difficult to navigate the fractal. I played a lot in 2D too: different coloring methods, tweakings, hybrids, and so on... I love this formula! thanks Sam! :-* Title: Re: Fractal expressionism Post by: s31415 on April 19, 2011, 11:34:52 PM Haha, you're welcome!
Title: Re: Fractal expressionism Post by: Kali on May 02, 2011, 08:26:13 AM You inspired me, Sam... take a look:
http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/ Title: Re: Fractal expressionism Post by: s31415 on May 02, 2011, 07:43:01 PM Yes, one can imagine a lot of formulas on this principle. What I find most interesting about your formula is that it has a direct 3d analogue. Looking forward to seeing more of the 3d version.
Title: Re: Fractal expressionism Post by: bib on May 02, 2011, 10:24:50 PM Having fun with Sam and Kali's ideas
Mandelbulb3Dv16{ O.....c....s/...3....22...UmJtUxhgx3.XWfy8PH3m1Ey80ElHiP6.wqs9M3FuL..v5rYgWzAO/k ................................aIXr78hVc.2........../..................y.2..... ................/MU//....6............E2.....opMMFmkG5nD/..........c./...w1.BnAH z.EnAngD1E../2.........wz0.......................................y1...sD...../.. .w1...sDFiuHJD9Ofw1K7jjzkQV3z0hij3SUjDmj2DmOPcbGavX2D8XXjwy9z.Hv5mrACyljks978.tj awneGKJXvFf3zQNChuITwXmD......I/......................sD..kz0................... ..............................MRAB.4qlo.kO5H1UoRAB.srlo.sV5H1.FSAB.............. .....................wzzz1.U..6.P....M4...EB....W....61....F....8/...I1....UJl22 ...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0. FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c.. zzzz.................................2U.8.kzzzD................................. /6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq 40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3................................. E.E..A....E.....I....A....kLklKMiJaFjl4N.IaQ.................................... ..............................zD................................................ ................................................................................ .....................2.....3.........w3HjR4B2/EOiN5............................. ..............................................................zD................ ................................................................................ ................................/....E/...k.....T34NYB2......................... ........................................kz1........wz.........zD................ ................................................................................ ............................................} Title: Re: Fractal expressionism Post by: bib on May 02, 2011, 10:53:28 PM Mandelbulb3Dv16{
O.....m....K0...s/...2.............2.1XEJNxTag/EdBHj78niyx114L.RNeovzKbDAjhvjZlD .................................x2e3kMGA.2........../..................y.2..... ................/g.0/....6EU0...K3...2E4.....UrITUYrtWoD/g./YJ8E...c//...w1.OaNa zIUaNadD1E../2.........szqAnAnAnAnyjOaNaNaNaty9..................y1...sD...../.. .w1...sDYsAIxzzzjz1..........WAbUdisqcljTcFzUvMS3t97C1JzzzzvzUNehUisqcljMaO9c9iB Ow1mQ0auWPX4zU2bVezzzzyD......2J0...j2................sD.2E.0................... ..............................MRRB.4qpp.kOLL1UoRRB.srpp.sVLL1.FSRB.............. .....................wwfk.kP.w7.m.....4....F....N1...I9....F....8/...k2w...UJlw. ...U.4MQIJlZD0MAmcLdS6piW16.0c..U1Cs.oklrlkCx9zjgPJOyyyDuz1...........U.8.kRWx2. 5Got8VlJKznH6.IPA/Jsz...........3MVAzfje3.U92G5Y3Ga3./b4JxvEF6/kvCf0iVAuK.A7/ckz jMXD.kpjTdSjU9yDOX3QOp/zrzHwTAUVlR5Vz4U.8.kzzzD................................. /6U0.wzzz1...................................ItRS/UBkM1.8mUWhl2.Tl3L..F4gK8X.g2I E/UwYMtS1/EI8/3.f4nW846.ZJKO.I/FUisL.k/6M.kHGRsUu/.NZd4.d.KX7S6.nAHA.2WPHeMR.UsQ L/EPwd7Wh/koF9B....y3q/.ee0k.1A.IJ3yAT2.wy5y3q/................................. E....M....E.....I....A....kLklKMiJaFjl4N........................................ ...................wz........................................................... ................................................................................ .....................2.....3.........wJEWB5K.656ExqRZ75......................... ..............................0E........kz9..................................... ................................................................................ ................................/....E/...E.....T3YMnZ3......................... ................................................................................ ................................................................................ ..........................................E.....I.........kL/7qQO/.............. ...................................................6./.......................... ................................................................................ .....................................................2.....3....2....wpQkVKNmJKO iN5............................................................................. ..............zD................................................................ ................................................................/....E/...k..... T34NYB2.................................................................kz1..... ...wz.........zD................................................................ ............................................................................} Title: Re: Fractal expressionism Post by: Kali on May 02, 2011, 10:59:49 PM Nice renders Bib!!
@Sam: you know, I really don't like the name I put on this, "Kaliset"... is not even a "set" I think. Do you mind if I use Kaliducks? :embarrass: Title: Re: Fractal expressionism Post by: s31415 on May 02, 2011, 11:17:17 PM Haha... whatever you like best!
Yes, I've tried to think a bit about the mathematical status of these space-filling fractals, and I'm not very sure yet. Title: Re: Fractal expressionism Post by: Jesse on May 03, 2011, 12:01:50 AM @bib: Nice renders! Unfortunately some formulas seems to have changed, so params might not work for all... the abs have now one parameter that is initialized more or less randomly, the value must be set to zero. You could also take the abs4d instead of all abs! And the Log4D seems to have changed too, dunno more about that. Cheers! |