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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > General Discussion > Fractal expressionism
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Author Topic: Fractal expressionism  (Read 8030 times)
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s31415
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« Reply #15 on: April 13, 2011, 07:32:12 PM »
Sure, I guess when an algorithm is published it's public domain.
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #16 on: April 13, 2011, 07:32:37 PM »
Quote from: bib on April 13, 2011, 05:48:11 PM
Quote from: Kali on April 13, 2011, 05:46:01 PM
What about a 3D version of Ducks?

LUCAAAAAA ?? (let's ask Darkbeam wink)

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 Azn

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! smiley

Have a nice day my friend Azn
« Last Edit: April 13, 2011, 07:35:44 PM by DarkBeam » Logged
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #17 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; yawning; tired
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Kali
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« Reply #18 on: April 19, 2011, 10:39:18 PM »
 cheesy



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!  kiss
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s31415
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« Reply #19 on: April 19, 2011, 11:34:52 PM »
Haha, you're welcome!
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Kali
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« Reply #20 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/
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s31415
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« Reply #21 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.
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bib
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At the borders...


100008697663777 @bib993
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« Reply #22 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................
................................................................................
............................................}

* 3Dducks3.jpg (170.53 KB, 800x600 - viewed 387 times.)
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bib
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« Reply #23 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................................................................
............................................................................}

* 3Dducks6.jpg (208.05 KB, 800x600 - viewed 370 times.)
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Kali
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« Reply #24 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
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s31415
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« Reply #25 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.
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Jesse
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« Reply #26 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!
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