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Author Topic: Jerusalem cube - can be made via KIFS?  (Read 6270 times)
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #30 on: December 04, 2012, 04:16:30 PM »

Yes Knighty; there is a plane that shows off the cut, like in the original Menger3 (that you later fixed, making MengerIFS cheesy ) but in normal circumstances it's not too disturbing angel

I will probably try your baird delta with pleasure, as always. I have also seen this gem of code

Code:
      //equilateral triangle symmetry (in order to duplicate the little copies)
      y=abs(y);
      t=2*min(0,x*sqrt(3)/2-y*1/2);
      x-=t*sqrt(3)/2; y+=t*1/2;

That should be also implemented as a standalone transform. A Beer Cup It should work like my PolyFolding but it is slow due to a trig formula...
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DarkBeam
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« Reply #31 on: December 04, 2012, 04:22:55 PM »

@Darkbeam:
In my previous reply, I was (indirectly) asking for a hollow (inverted) BoxIFS shape to be used in difs. Possible?

Already tried to set a negative scale? Should work. Azn

Mandelbulb3Dv18{
b.....S....O/.../....2....U4nrZayiC4.T2j7duEiR3EjTrp9NG6..IZ9wuVcuUyzSDBIhxqivzD
................................9BGHRY2MTz1........A./..................y.2...wD
...Uz.....U3..../M.0/.....EP....8.....E3.....oASKrbaH8sD/..........m/dkpXmn/...U
z.....kD12../..........wz..................................u1....y1...sD...../..
.z1...sD4krzSz2y.yXbzXFWWVrMzcnr3E5OTQqj09BuTZraXuXN.yAVGe4Tzkt0xUOGjTrDxOxqS2bC
ixXcZUmHCqRRzmE1i..FpbrD......o...............sD.6....sD..E.....................
.............oAnAt1...sD....z.rbv4.2UiP.k0ui/.Jcv4.wViP.E8ui/.ncv4....../....k1.
..................kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD4ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....2....E.....I....o....UMjVLG4B3.U.pPrJaQ.............................sU1....
/6U./2.............wz.........zD........kznAnAnAnAnoz0..........................
...................................wz...................kz1........wz...........
........................}

then grin

Mandelbulb3Dv18{
b.....S....O/...w....2....kMmjRzUzhtzmacJEAI300Eu.d9Rg75AzfTCqqvSi0pzI/HiDLdQ9xj
................................FbGbNwM1X.2........Y./........2E.......UK/2...wD
...Uz.....k2..../M.0/.....Um....g.....E3.....wVoUHsQLunD/..........m/dkpXm1....U
z.....kD12../..........wz..................................u1....y1...sD...../..
.z1...sDlzoX1JXwvwXI4awSRf77z0idq3JRfjljhViBHzzjYt13mR/3eRGAzeJ1eTwLIZnDULw3Aers
cwf/E74F3DmBzWfXFs2sKxmj......25..............sD.6....sD..E.....................
.............oAnAt1...sD......rbv4.2UiP.k0ui/.Jcv4.wViP.E8ui/.ncv4......B....2..
..................kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD4ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E6../6....E.....I....o....UMjVLG4B3.U.pPrJaQ.............................sU1....
/6U./2.............wz.........zD........kzH6yM6W6W6xz0..........................
...................................wz...................kz1........wz...........
.....................2.....3....5....oINiRKNmZYFH/..............................
.....MU/4....................U.E........kz1........wz.........yD................
................................................................................
................................}
« Last Edit: December 04, 2012, 04:35:25 PM by DarkBeam » Logged

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bib
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« Reply #32 on: December 04, 2012, 05:03:47 PM »

Oops! I've just checked the DE And it turns out that there are discontinuities which will cause some sand artifacts. Sorry for that.

No prob, I love M3D sand effect with a lot of AA
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M Benesi
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« Reply #33 on: December 04, 2012, 07:42:25 PM »

Oops! I've just checked the DE And it turns out that there are discontinuities which will cause some sand artifacts. Sorry for that.

  Here's a non DE Baird Delta.  Can set bailout to 1, but it's a bit fuzzier then, unless one does additional samples (the "natural" bailout value is 1...).  It's set at 3.

  Thanks for the informative post.  Need to find some <mathematical> object to play with.  cheesy




* Baird-Delta04 no DE.frag (2.44 KB - downloaded 220 times.)
« Last Edit: December 04, 2012, 07:44:20 PM by M Benesi » Logged

knighty
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« Reply #34 on: December 04, 2012, 07:55:29 PM »

@Benessi: I was talking about the "Jerusalem cross".  smiley

@bib: between your hands, the sand artifact becomes a wonderful artistic effect. I remember some of your work which use it nicely.

@DarkBeam: Ah! thanks. cool! but there still is a little problem   evil: When using multiple iterations the copies belonging to even iteration number are not hollow.  fiery
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David Makin
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« Reply #35 on: December 04, 2012, 10:14:36 PM »

Just to point out that one way around the "too many parameters" problem is turn KIFS into a form of LRKIFS i.e. language restricted KIFS.

For those who don't know: LRIFS is language restricted IFS where the application of transforms is controlled by a programmatic method e.g. using cellular-automata style variation - this could be applied to the rules in KIFS such that the user has a small set of instructions controlling the transforms used (and when they're used).
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bib
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« Reply #36 on: December 04, 2012, 10:43:16 PM »

When exporting the voxel in M3D, the artifacts are very visible, I can't make a proper OBJ file.
Each cross at the end of the arm of the bigger cross is too different from the adjacent ones.


* jcube-1600000020.png (16.69 KB, 500x500 - viewed 702 times.)

* jcube.jpg (74.36 KB, 493x473 - viewed 609 times.)
« Last Edit: December 04, 2012, 10:58:32 PM by bib » Logged

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bib
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« Reply #37 on: December 05, 2012, 02:20:44 AM »


http://www.shapeways.com/model/813222/jerusalem-cube-4cm.html
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knighty
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« Reply #38 on: December 05, 2012, 10:40:02 AM »

 undecided Don't know. I don't have the same problem.
Here is an evaldraw script in case one wants to check the DE:
Code:
//use with evaldraw: http://advsys.net/ken/download.htm
(x,y){
   JC4(x,y,mousx*0.001,sqrt(2)-1)^0.25//the "^0.25" is just for better contrast
   //(JC4(x,y,mousx*0.00+1,sqrt(2)-1)<0.005)-0.5
}
static MI=10;
JC4(x,y,z,alpha){
   scl=(alpha+2);
   scl1=scl/alpha;
   a=1/scl1;
   r=x*x+y*y+z*z;dd=1;
   for(i=0;i<MI && r<10000;i++){
      x=abs(x);y=abs(y);z=abs(z);
      if(x-y<0){x1=y;y=x;x=x1;}
      if(x-z<0){x1=z;z=x;x=x1;}
      if(y-z<0){y1=z;z=y;y=y1;}
     
      if(z<a && y>1-3*a+z){
         x-=1;y-=1;
         x*=scl1;y*=scl1;z*=scl1;dd*=scl1;
         x+=1;y+=1;
      }else{
         x-=1;y-=1;z-=1;
         x*=scl;y*=scl;z*=scl;dd*=scl;
         x+=1;y+=1;z+=1;
      }
      r=x*x+y*y+z*z;
   }
   (sqrt(r)-1.75)/dd
}
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DarkBeam
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« Reply #39 on: December 05, 2012, 11:05:18 AM »

I don't know... And I won't be able to use my pc soon for some time
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David Makin
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« Reply #40 on: December 05, 2012, 01:11:51 PM »

OT - for Darkbeam - a friend of mine has BT optical (obviously he lives in a much more populous area than me, it's not likely to be available here for maybe a decade!!):

http://speedtest.net/result/2298282143.png
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M Benesi
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« Reply #41 on: December 07, 2012, 06:02:14 AM »

  Code does seem to have more iterations around the ends of the crosses- this is even more prevalent at the ends of the big cross.  This is in a non-DE version, done with the code above.



code for Jerusalem math- constants set elsewhere
Code:
vec3 JerusalemX (vec3 z) {

  
z = abs(z);
z.xy=Rot2(z.xy, xyAng);      //Rot2 is a rotation around the origin
if (z.x<z.y){ z.xy = z.yx;}    
z.xz=Rot2(z.xz, xzAng);
if (z.x< z.z){ z.xz = z.zx;}
z.yz=Rot2(z.yz, yzAng);
if (z.y<z.z){ z.yz = z.zy;}
      
      if (z.z<a && z.y>1.-3.*a+z.z){
         z.x-=OffSet.x;z.y-=OffSet.y; //OffSet is the OffSet variable from the Menger formula
         z*=scl1; // it is set at 1,1,1
         z.x+=OffSet.x;z.y+=OffSet.y;
      } else {
         z-=OffSet;
         z*=scl;
        z+=OffSet;
      }
return (z);
}
« Last Edit: December 07, 2012, 06:05:28 AM by M Benesi » Logged

knighty
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« Reply #42 on: December 07, 2012, 07:42:44 PM »

That is normal behaviour: the "corners" are copies of the whole cube with scale sqrt(2)-1 while the little cubes at the edges are copies with scale (sqrt(2)-1)^2.
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knighty
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« Reply #43 on: December 07, 2012, 08:05:33 PM »

BTW!
the only way IMHO to have a correct DE is to go for (classic) IFS (and LRIFS) or a mix between KIFS and IFS. Obtaining the DE for IFS requires a priority queue. I have successfully adapted Hart's -IFS raytracing- method to return DE instead. My implementation is experimental and use a simple array as priority queue therefore it is slow.


* IFS-dist.JPG (25.88 KB, 640x480 - viewed 490 times.)
* IFS-dist22.kc.txt (3.25 KB - downloaded 270 times.)
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M Benesi
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« Reply #44 on: December 07, 2012, 08:37:22 PM »

That is normal behaviour: the "corners" are copies of the whole cube with scale sqrt(2)-1 while the little cubes at the edges are copies with scale (sqrt(2)-1)^2.

  The author's Jerusalem Cross look like he only targets specific sizes of cross each iteration.  Might be fun figuring out how to do that.
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