Title: Kaliset + Rotations Post by: Kali on May 26, 2011, 03:32:12 PM Hi all, I will be posting some images and M3D parameters of my formula Kaliset with added rotations. I think it could be of interest, but I don't want to flood the gallery with images so I'll be posting them here as I get nice results.
For quick renders, the images will be in "video" quality of M3D, grayscale colors and no antialiasing (the idea is to show a preview and sharing params) I'm posting the first images soon... enjoy! :dink: Title: Re: Kaliset + Rotations Post by: Kali on May 26, 2011, 04:04:00 PM One of the issues of the implementation of my formula in M3D is the need of using "fixed zoom & steps" in the navi window, otherwise it don't work properly.
This option allows you to "walk" through the fractal, making cuts as you move (so you must use zoom for close-ups). This just made me discover that some of this fractals are hollow, so they are like a "membrane". Both inner and outer surfaces are worth exploring. Mandelbulb3Dv17{ P.....c....s/...61....2....PQVkPvo.1.n3ECHaUfm4ESiT65WNGtzfigbn8HbLyzWkdz4naxFyj ................................uJILslsJqznAnAnAnAnyz...................y.2..... ................/MU/.....6.i/...v6....Ed.....wvDSz.vECqD/..zCKrD...c//...w1....U zEEnAngD1E../2UaNaNaNaNizeNaNaNaNaxj.............................y1...sD...../.. .w1...oDhC86m36YRxX.BrR6KuGJzmRvtmEiWnojSOFNDXun0xHiF9PTNTlFzOoQa4d.M6qDa4XXfAMq Lx9Q9XQMeygLzyv8KDBwComj.....w1u/........2....kD.2....sD..kz0................... ...........sz0................ORj6.CqxW.EPr90UqRj6..sxW.MWr90.HSj6.............. ................N....wzzz5.O..6.4/...s6....9....g0...62...k/....v....Qn...ECvqJ/ /34U..8cUyDcU0uz....z1Ak.n9/0Emzzzzz.gohlLBfvrzD/0BehOeEWzH7sse0dENxz4E.I..gy21. 8LsffaWeYzPCR8Zc4xRczEWfzHx6d2yD/2.3.ktbN/UNIXBzAbNvz0CwQOr9PExj.ezYfTLkRzH/UEmz rVLE.......................H1eQUVACtzKl386kZFc8..IEjZNvqN.w675azqvNfzi3cbtUapEzD Z6W0zL3O.0.qgzuvb.m..dwTjVa38cpjh/PoYQ161.A...8cU0.cU08.zz/cU08.U08c.szDU08c..8c U0EzT/8cU0.cU08.Qs5cU08.U08c..bTU08c..8cU0.ly/8cU0.cU08.Mw5cU08.U08c.kqTU08c..8c U0.kz/8cU0.cU08...E.....zzF..Y/.yzn5/A..xz3..s/..ooFTRXAlIX98/pF.wZMtxJFHxY9e/rN E....6....E.....I....A....kLGx4RVFLN.................................MU/4....... ..................cF./.......O2E.......U4/2..................................... ................................................................................ .....................2.....3....0....gIMgZqQZFrQl.kRZ75..6LPm................... ..U/..........................zD................................................ ...................................wz........................................... ................................} Title: Re: Kaliset + Rotations Post by: Kali on May 26, 2011, 04:27:54 PM A close up of a region in the inner surface (same parameters as previous post)
Title: Re: Kaliset + Rotations Post by: Kali on May 26, 2011, 06:16:19 PM An strange object and it's insides.
Mandelbulb3Dv17{ P.....c....s/...61....2....afEmuWpX..rauubO6sG1EiMFZGZqccwPCzLtdMwCTzCtNUyUSHszj ........................................Y.InAnAnAnAzz...................7/2..... ................/MU/.....6ke9...n3....Ed.....wwUvCfRPLnD/..zCKrD...c//...w1....U zEUaNadD1E../2UaNaNaNaNmzeNaNaNaNawjOaNaNaNa7z9..................y1...sD...../.. .w1...sD3q0W0t77xw1..........cm2lgEjTTajR57b7wRwcs1pP42SlGFDzohf54AEntjDmn9JI3fo bt1dMK/l.Bbzy4Y4FLLgIonD.....w1M0........2....kD.2....sD..kz0................... ..............................ORj6.CqxW.EPr90UqRj6..sxW.MWr90.HSj6.............. ................9....wzzz1.C.U2.51...Q3...EA....p....I1...k/....v....Anu..ECvq32 Tc4U..8cUyDcU0uz....z18cUm9.kc..qOfh.oklrlkCx9zD8LsffaWeYz1..........2U.8.UQgk0. IwUmc2beYz1RdA8E5Exwz0........../2.3.ktbN/UNIXBzAbNvz0CwQOr9PExj.ezYfTLkRzH/UEmz rVLE.......................H1eQUVACtzKl386kZFc8..IEjZNvqN.w675azqvNfzi3cbtUapEzD Z6W0zL3O.0.qgzuvb.m..dwTjVa38cpjh/PoYQ161.A...8cU0.cU08.zz/cU08.U08c.szD......8c U0EzT/8cU0.cU08.Qs5cU08.U08c..bTU08c..8cU0.ly/8cU0.cU08.Mw5cU08.U08c.kqTU08c..8c U0.kz/8cU0.cU08....cU08.zz/cU08.yz1.....xz3cU08..ooFTRXAlIX98/pF.wZMtxJFHxY9e/rN E....6....E.....I....A....kLGx4RVFLN.................................MU/4....... ..................cF./.......O2E.......UK/A..................................... ................................................................................ .....................2.....3....0....gIMgZqQZFrQl.kRZ75..6LPm................... ..U/..........................zDaM8feGUhtB1..................................... ...................................wz........................................... ................................} Title: Re: Kaliset + Rotations Post by: Kali on May 28, 2011, 05:03:11 AM I added some color to this quick renders... I don't liked the grayscale ones, coloring helps to enhance the 3D effect (depth, surface detail)
Also this looks like some reptilian organic structure, so I used green for skin and red for internal organs (viewer discretion advised) ;D Mandelbulb3Dv17{ P.....c....s/...g2....2..............1.......s1E................................ ........................................I.oAnAnAnAnyz...................7/2..... ................/MU/.....AkAB...8/....Ed.....wwUvCfRPLoD/..zCKrD...c//...w1....U zEEnAngD1E../2kAnAnAnAnozOaNaNaNaNxjOaNaNaNa7z9..................y1...sD...../.. .w1...oDYsAIxzzzjzXlTplE2uS.z6P/A0u8WWljTcFzUvMS3t93npRyx6Vvz2e2uzY5WLxDMaO9c9iB OwHvTDWHS6Spzy7iLRTDGsyD.....wXy/........2....kD.2....sD..kz0................... ..UNaNaNaNatz0................ORq6.CqNX.EPbB0UqRq6..sNX.MWbB0.HSq6.............. ................r1....6U.0ES....P....A0...U7....O....g4...k/....v....Ymm...UtzJY W75U..KTF/6.h..U.....0...k96/c..zzzz.EmYEkti4xwj5Got8VlJaz9..........EE.IwDbwl3. GhKls45cBz1n9kfzdI.rz6GFXSR0WVzj2/mBzvJ7W.EvgOB.xkAgzmgvTBKSgDvjp.h0nQbEXzH/UEmz rVLE.......................H1eQUVACtzKl386kZFc8..IEjZNvqN.w675azqvNfzi3cbtUapEzD Z6W0zL3O.0.qgzuvb.m..dwTjVa38cpjh/PoYQ161.A..M5Vx/EgrG9.zbmS.u4.elqM.wzI0acU.YZK N/kyxFLRz/UHCB3.VzrW/05..0sT.IyTktrT.6KMV/kuzx4Wx/kTEW6.kz5X.07.18sU.MzTFuaV.6uY Q0kyz7cY.0kl7TA....cU08.zz/cU08.yz1cU08.xz3cU08..ooFTRXAlIX98/pF.wZMtxJFHxY9e/rN E....6....E.....I....6....kGVlKOnJ4Rn31.rJaQ..UQh71............................. ...................wzMWdge8/qarA................................................ ........................kz1..................................................... .....................2.....3....1....wZIjFLMoJ4................................. 4MU/.........................E/k.......U4/A........B./.......................... ................................................................................ ................................} Title: Re: Kaliset + Rotations Post by: Jesse on May 29, 2011, 02:08:55 AM I think this is very cool, the iterated sphere inversion leads to a fractal surface without any volume (imo).
Could be a special fractal class maybe? Title: Re: Kaliset + Rotations Post by: madaussie on May 29, 2011, 07:31:45 AM Whilst I haven't yet tried the rotations I have managed to create a Mandelbulb which has two distinct images with one seemingly inside the other. The initial formula involved the LaliLincombSSE2sm. A lot of playing around without knowing quite what the outcome might be. Anyhow the parameter is below:
Mandelbulb3Dv17{ P.....S....O/...w....2A..............1.......s1E................................ ........................................kz1........Y./..................y.2..... ................/M.3/....6Eq4...n.....E4.....omEQgisq6rD/..........c./...w1.BnAn x.EnAnQD1E../2...................................................y1...sD...../.. .wHnAnQDpiOMGrTBjzXf868.cuUmzo8Kt9ENHLvDLWlU2Eb.0zfkMuHTFVOozMZJEsNChtyDu.DYHSyk 3znQ25LiexUvzicvPCM6CAxD......2V1.............kD.2....sD.6kz0................... ..............................ORI9.CqFh.EP5p0UqRI9..sFh.MW5p0.HSI9.............. .....................wzzz1.U..6.P....k1...EB....L....c3....F....8/...I1....UJl32 ...U.eoZgzjdqZpz8R7vzPeRN/6.0c..zzzz............5wyBIC4OWz1..........2k.8.kXWF1. QvM93P58iz9GMmnWK2zwz0........../6U0.wzzz1................................E.0c.. zzzz.................................2U.8.kzzzD................................. /6U0.wzzz1...................................QoFx0......jpUfEe4.tANU.6i4ve9G..gS q/UIcEDul1kzE0A.QHHcJa7......EaEkyth......EMDBeH00......yj3MAZ2......cDOISPK.... ..EaqVaek0.........U./0.zz/6FG1.yzHkqs/.xzZteKA................................. E....A....E.....I....2....kGVlKOAZaP1xKPWBpI37nQh/...................6..4....... ..................U6./........zj................................................ ................................................................................ .....................2...../....1....2IPVdLOiR460x4S............................ .Qk0...........................E........Uz1........wz.........yD................ ................................................................................ ................................/....E/....0....I34PdB5JkV5.g71................. ....................0...................kz9........wz........................... ...wz..............................6.NaNaNaNaNzD................................ ............................................} I haven't posted the image yet in the gallery as I am in the process of removing some little artifacts in PS. If someone can explain the workings of the parameter I would love to hear it. Madaussie Title: Re: Kaliset + Rotations Post by: Kali on May 29, 2011, 03:05:01 PM I think this is very cool, the iterated sphere inversion leads to a fractal surface without any volume (imo). Could be a special fractal class maybe? Thanks, Jesse. Don't know exactly, I think it's maybe a shell from Tglad's notation. btw, why normal navi mode doesn't work with this? @madaussie: Cool, I've done some images like that with my formula "KaliLinComb" (is not "Lali", lol :D). It produces weird results in combinations (or no results at all) because of the formula variables being handled by the program in a different way as other formulas (at least is what Jesse told me, but he can explain it better) Title: Re: Kaliset + Rotations Post by: Tglad on May 30, 2011, 02:08:41 AM A closed undulating surface... needs some thought...
The classes as in http://sites.google.com/site/mandelbox/what-class-of-fractal (http://sites.google.com/site/mandelbox/what-class-of-fractal) are like the building blocks, so you can combine them, for example this (http://www.thesea.org/images/sea_sponge_thumb.jpg) is a tree of void-sponge, a tree class where the solid part is made of a void (no mass) sponge. Similarly a landscape like this (http://wpcontent.answcdn.com/wikipedia/commons/thumb/6/6e/FractalLandscape.jpg/220px-FractalLandscape.jpg) has hills on hills, and dips in dips, so it is a tree of a shell, or a shell of a tree, or just shell+tree. So if you ignore the fact that it is hollow then it is a shell+tree as its surface shows recursively concave and recursively convex areas. So the fractal itself is the surface of a shell+tree. More correctly you could say it is a void-foam with no children (i.e. a single closed surface), who's surface shape happens to be the surface shape of a shell+tree. But the table doesn't really classify single surfaces directly, similarly you would have to say that a koch curve is a tree with no children (i.e. a line) who's shape happens to be the shape of the border of a 2d tree. Not an easy one :) maybe there exists a classification specially for undulating surfaces. Title: Re: Kaliset + Rotations Post by: Tglad on June 01, 2011, 01:31:25 AM This fractal of yours is really interesting
(http://www.fractalforums.com/index.php?action=dlattach;topic=7407.0;attach=5249;image) the top is a tree structure, lumps on larger lumps, and the bottom is a shell, hollows in larger hollows. The two pieces in between clearly are a mixture of both, and it appears as having ridges and valleys. Much like landscapes: (http://www.china-mike.com/wp-content/uploads/2011/01/great-wall-panorama3-small.jpg) And the surface of rocks- (http://upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Big_Rock_in_a_Field.jpg/800px-Big_Rock_in_a_Field.jpg) But you don't tend to get this by making a simple fractal terrain of bumps and dips: (http://jesseoconnor.com/projects/pacman3d/terrain2.jpg) There must be a certain correspondence between the bumps and dips which produce ridges. Would be an interesting thing to investigate, it could produce nicer terrain fractals. Title: Re: Kaliset + Rotations Post by: Kali on June 01, 2011, 06:55:02 AM Good observation. Here is a close up of the "terrain". Indeed, you can see the mix of the structures from above and below.
(http://img20.imageshack.us/img20/5930/terrains.jpg) Title: Re: Kaliset + Rotations Post by: Kali on June 07, 2011, 04:14:16 AM Speaking of terrain generators, this is using "genIFS", a formula Jesse included in the latest Mandelbulb3D, based on my idea of "simplified KIFS" (abs,rotation,scale,translation). In this case, Jesse added an "offset" parameter (additional translation), then add C... this makes a "mandelbrot mode" KIFS, and some of the results can be really interesting. I was doing the same in a 2D KIFS formula I made for Ultrafractal, to preview the patterns and then pick Julias. But the 3D version surprised me, and it's also very fast: (http://img52.imageshack.us/img52/1297/paisajem.jpg) Mandelbulb3Dv17{ P.....Y/..ki1...w.....6...E8/8237WHuzejuV9cd.szDbz74PDgAkz1bn2VbTEumzeaWiIDXn8yj ................................Ygc9nbIHm.2........A./..................y.2..... ...............././0/....6ko0...63....E2.....AXURvfgPAlD/..........c./...w1.OaNa z.UaNadD1E..0..........szCnAnAnAnAwj........Ez9..................y1...sD...../.. .w1...kDvk4NMviSUvfcOBEgANk7zsBim08LIYkjEH1W0edHbwfZbD7Oeccwy0a9aIJnt8kjAar734.T 2wvirqgNrcu/zco/lZdAFOmD......If1.............kD.2....sD/.kz.................... ..............................OR67.CqVY.EP5G0UqR67..sVY.MW5G0.HS67.............. ................f....ENZe/UO..3.h....Q2...EF....c.....2...E4....U....oom...UJxZ1 6E/U.y2UsVPF/3Gi4OvjL4m7m.6..c..Rjhm.Io.Tci/2UyjX6HNL1YPWz1.........../.G2.Wkx2. 3Bk5eP./sz1skndRjg/pzEaBmE031C/E2.UMzHAlc0ER3g3Tgcxzz..DMdzxWMyDRLLuiTXVNyH.0c.. zzzz.................................2U.8.kzzzD................................. /6U0.wzzz1...................................I5Uq/UMV/4.zbGT2m6.DzQo.wzIp36S..2E z.kyxt5Ry/kl/LA.VzbS5q5.ZaOd.IyTtZbT.UtZN0kuzlMVw/Um7XA.kz5T8y5.tqPi.MzTrJcW.2Al 31kyzZsRv/U9bU0....cU08.zz/cU08.yz1cU08.xz3cU08................................. E....2....E.....I....c....kNZtKG4B3.U.pPrJaQ..........................U.06E./2U/ 4M........Uf53iSIsOxz0..................kz1........wz.........zj........kz9..... ...wz0.......s1k........I.2........3./.......................................... ........................} I guess that adding a "randomness" factor should make even better terrains. I'm currently trying that on 2D KIFS patterns with good results. |