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Author Topic: Kaliset + Rotations  (Read 10878 times)
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Kali
Fractal Supremo
*****
Posts: 1138


« 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!  wink
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Kali
Fractal Supremo
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Posts: 1138


« Reply #1 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...........................................
................................}


* 01.jpg (133.45 KB, 640x480 - viewed 497 times.)
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Kali
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Posts: 1138


« Reply #2 on: May 26, 2011, 04:27:54 PM »

A close up of a region in the inner surface (same parameters as previous post)


* 02.jpg (213.07 KB, 640x480 - viewed 576 times.)
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Kali
Fractal Supremo
*****
Posts: 1138


« Reply #3 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...........................................
................................}


* 03.jpg (104.31 KB, 640x480 - viewed 578 times.)

* 04.jpg (90.35 KB, 512x384 - viewed 505 times.)
« Last Edit: May 29, 2011, 03:37:56 AM by Kali » Logged

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Kali
Fractal Supremo
*****
Posts: 1138


« Reply #4 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)   grin

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./..........................
................................................................................
................................}


* 09.jpg (91.18 KB, 640x480 - viewed 529 times.)

* 10.jpg (100.41 KB, 640x480 - viewed 533 times.)
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Jesse
Download Section
Fractal Schemer
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Posts: 1013


« Reply #5 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?
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madaussie
Alien
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Posts: 29


« Reply #6 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
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Kali
Fractal Supremo
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Posts: 1138


« Reply #7 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 cheesy). 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)

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Tglad
Fractal Molossus
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« Reply #8 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 are like the building blocks, so you can combine them, for example this

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

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 smiley maybe there exists a classification specially for undulating surfaces.
« Last Edit: May 30, 2011, 02:14:59 AM by Tglad » Logged
Tglad
Fractal Molossus
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Posts: 703


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« Reply #9 on: June 01, 2011, 01:31:25 AM »

This fractal of yours is really interesting

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:

And the surface of rocks-


But you don't tend to get this by making a simple fractal terrain of bumps and dips:

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.
« Last Edit: June 01, 2011, 01:37:03 AM by Tglad » Logged
Kali
Fractal Supremo
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Posts: 1138


« Reply #10 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.

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Kali
Fractal Supremo
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Posts: 1138


« Reply #11 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:



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.


« Last Edit: June 07, 2011, 04:26:25 AM by Kali » Logged

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