Print Page - Jerusalem cube - can be made via KIFS?

Title: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on November 30, 2012, 07:06:34 PM

Looks a promising fractal.

http://alt-fractals.blogspot.it/2011/08/jerusalem-cube.html

I can see that it does not have an uniform scale btw, so I guess it's impossible to convert it in simple KIFS, without breaking strict continuity of space? :sad1:

Thanks for deep thoughts :beer:

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: M Benesi on December 01, 2012, 12:02:23 AM

I've seen something similar while messing with Menger Cubes or Koch Cubes... not sure about the specifics of the formula I used. Did a quick try, and didn't find it.

All right. I've gotta convert it (the Menger) to a NON DE formula to make the render sharper, but for now, use the Menger KIFS in Fragmentarium. Rotation angle= 45 , rotate around 1,0,0 (the x axis, I suppose). You have cut outs, however, where the Menger holes are rotated to. Need to move the rotation...

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: cKleinhuis on December 01, 2012, 12:04:37 AM

why is it using non rational numbers ?! because the cube is divided by 5 instead of 3 ?!

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: M Benesi on December 01, 2012, 12:41:05 AM

Nah.. Cube, with side length 1 has a diagonal of $\sqrt{2}$ . In fact, all diagonals of a square are side length * $\sqrt{2}$ ....

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: kram1032 on December 01, 2012, 02:38:45 AM

That's pretty :)

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 01, 2012, 10:57:28 AM

Quote from: cKleinhuis on December 01, 2012, 12:04:37 AM

why is it using non rational numbers ?! because the cube is divided by 5 instead of 3 ?!

The holes and cubes of a menger sponge are equal in size, BUT! look carefully the JCube... Some cubes are smaller some bigger (just in the in the 1st iter!), that means that you can not multiply all components by a scaling factor like in normal fractals (3 or 2 usually). When this happens normally you need some cuts and this is bad whenever you try to add rotations somewhere! :sad1:

:beer:

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 01, 2012, 11:03:58 AM

Quick sketch with paint ;D

Refer to http://alt-fractals.blogspot.it/2011/11/jerusalem-square.html for more accurate reference :D

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: David Makin on December 01, 2012, 11:06:36 AM

Just work out the smallest sub-cube that the Jcube can be made from correctly and use as many plain transforms with that scale as necessary.
e.g. if it had 2 uniform holes (with all solid cubes the same size) at the 1st level then it would be the same as the standard Menger but with 5*5*5 transforms with scale 1/5, if 3 at the first level then 7*7*7 with scale 1/7 etc. - obviously with uneven sizes of holes and/or solids much smaller sub-cubes may be necessary although perhaps this could be avoided with adjustment of scale of the transforms maybe based on depth in the tree....

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 01, 2012, 11:12:57 AM

Quote from: David Makin on December 01, 2012, 11:06:36 AM

But KIFS just use "simple" transforms like in this Menger sponge ^-^ idk about "tree depth" ;D

Code:

   for(i=0;i<MI && r<bailout;i++){
      rotate1(x,y,z);

      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;}

      rotate2(x,y,z);
    
      x=scale*x-CX*(scale-1);
      y=scale*y-CY*(scale-1);
      z=scale*z;
      if(z>0.5*CZ*(scale-1)) z-=CZ*(scale-1);
      
      r=x*x+y*y+z*z;
   }

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: David Makin on December 01, 2012, 11:14:06 AM

Tree depth==iteration count in KIFS ;)
However I just realised that even KFS could use different scales based on location....

Personally I'm interested to see if anyone can come up with a fast way to render a finite-level "not" the Menger Sponge say "not" a level 4 Menger for instance :)

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 01, 2012, 11:16:18 AM

Quote from: David Makin on December 01, 2012, 11:14:06 AM

Tree depth==iteration count in KIFS ;)

Things may become hard to handle in hybrids? :dink: Itercount can not tell you the truth :embarrass:

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: David Makin on December 01, 2012, 12:48:13 PM

Quote from: DarkBeam on December 01, 2012, 11:16:18 AM

Things may become hard to handle in hybrids? :dink: Itercount can not tell you the truth :embarrass:

Depends on the type of hybrid ;)
If not every iteration of the entire hybrid includes the "sponge" then a separate count would be required just to count iterations for which the "sponge" is used.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty on December 02, 2012, 08:22:21 PM

I can't get a KIFS too! :-\
Here is what I get:

Code:

static scl=1/(sqrt(2)-1) /*=1+sqrt(2)*/, a=1-2*(sqrt(2)-1);
JC3(x,y,z){
   r=x*x+y*y+z*z;dd=1;
   for(i=0;i<MI && r<100;i++){
      x=abs(x);y=abs(y);z=abs(z);
      if(x<y){t=x;x=y;y=t;}
      if(z<x){t=z;z=x;x=t;}
      if(x<y){t=x;x=y;y=t;}
      if(y<a && x>1-2*a+y-a){
         x-=1;z-=1;
         x*=scl*scl;y*=scl*scl;z*=scl*scl;dd*=scl*scl;
         x+=1;z+=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
}

(BTW, in reply #6 picture, if the big square size is 1 we have:
Scale2=Scale1^2.
that means that: Scale1^2+2*Scale1-1=0.
the correct value is: Scale1=sqrt(2)-1. which is the positive solution the the equation above. O0)

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: Alef on December 03, 2012, 08:05:59 AM

Wov, a Vaticane Cube. This is one of the interesting new fractal ever. Probably it don't offers much variants, but this shape have deep cultural and religious background what makes it attractive.

Maybe two sierpinsky triangles making this would be pretty interesting thing.
(http://www.reconnections.net/movmerkaba.gif)

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 03, 2012, 10:15:10 AM

Quote from: knighty on December 02, 2012, 08:22:21 PM

I can't get a KIFS too! :-\
Here is what I get:

Code:

static scl=1/(sqrt(2)-1) /*=1+sqrt(2)*/, a=1-2*(sqrt(2)-1);
JC3(x,y,z){
   r=x*x+y*y+z*z;dd=1;
   for(i=0;i<MI && r<100;i++){
      x=abs(x);y=abs(y);z=abs(z);
      if(x<y){t=x;x=y;y=t;}
      if(z<x){t=z;z=x;x=t;}
      if(x<y){t=x;x=y;y=t;}
      if(y<a && x>1-2*a+y-a){
         x-=1;z-=1;
         x*=scl*scl;y*=scl*scl;z*=scl*scl;dd*=scl*scl;
         x+=1;z+=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
}

KNIGHTY!!! ;D ;D ;D How in the world you are always able to solve all problems! Your brain is a treasure chest! I adore it! I am envioussss! :'( :'( :'(

I wonder if you are also able to make a "general" version that calculate the limit, and the other scale, so that Scale1 is a user parameter. Other possible params are of course Cx, Cy, Cz like the other Menger. :dink: Even if it will not support rotates it will be surely appreciated from the MB3D folks!!! :beer: :beer: :beer:

In other words; a = function(scl) and scl2 = function(scl) instead of a fixed value :D

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 03, 2012, 10:20:10 AM

Another great potential fractal is this, should be easy to do in KIFS (single scale, continuous etc) but I can't find out... :embarrass:

http://fav.me/d4l5hf0

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: cKleinhuis on December 03, 2012, 10:23:26 AM

the mengers .... i implemented a hybrid menger with random distribution of holes 10 years ago in my fractalmovies.com screensaver,
it is using opengl, but might not run under win7 ...
http://fractalmovies.com/index.php?/archives/2-Fractalmovies.com-Screen-Saver.html

all sorts of mengers could be made, basically you could do the whole alphabet on the 3x3x3 cube .... ;)

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: Alef on December 03, 2012, 10:46:25 AM

Quote from: DarkBeam on December 03, 2012, 10:15:10 AM

I wonder if you are also able to make a "general" version that calculate the limit, and the other scale, so that Scale1 is a user parameter. Other possible params are of course Cx, Cy, Cz like the other Menger. :dink: Even if it will not support rotates it will be surely appreciated from the MB3D folks!!! :beer: :beer: :beer:

Parameters sometimes could be too much. When they are visualisated and with tips like in UF, its more easey, but if there are 10 windows with numbers it loses usability for most of the folks not so good with PC.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 03, 2012, 11:00:51 AM

Quote from: cKleinhuis on December 03, 2012, 10:23:26 AM

Yes, using the classic theory. (Allowing discontinuity)

Kifs are more complicated because you need a continuous spatial function so in hybrids and for every rotation you don't see any cut. :dink:

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 03, 2012, 12:27:52 PM

Quote from: Alef on December 03, 2012, 10:46:25 AM

Hey, just scale (the other scale is automatic), cx,cy,cz, plus cx2,cy2,cz2, is not that much :dink:

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: kram1032 on December 03, 2012, 01:35:43 PM

I like the fractal H. It looks like a scaffold of a building. I wonder what the final building will look like...

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty on December 03, 2012, 03:14:55 PM

Quote

How in the world you are always able to solve all problems!

:embarrass:
Unfortunately, that's not true.

Code:

I wonder if you are also able to make a "general" version that calculate the limit, and the other scale, so that Scale1 is a user parameter.

Code:

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<100;i++){
      x=abs(x);y=abs(y);z=abs(z);
      if(x<y){t=x;x=y;y=t;}
      if(z<x){t=z;z=x;x=t;}
      if(x<y){t=x;x=y;y=t;}

      if(y<a && x>1-3*a+y){
         x-=1;z-=1;
         x*=scl1;y*=scl1;z*=scl1;dd*=scl1;
         x+=1;z+=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
}

You get a menger sponge when alpha==1. Remember, this is not a KIFS. The continuity (of the orbits) is broken even if the returned DE is continuous thanks to a suitable cut (the "if(y<a && x>1-3*a+y)..."), but it could be impossible to find a simple one. Using this formula in a hybrid will almost certainly introduce discontinuity artifacts.

The H-Menger doesn't seem to be a KIFS either. It could be obtained by using the "half eaten menger" thechnique. Those could easily be made in MB3D with DIFS in DECombinate mode ("Ma" comb.) if there were "hollow" primitives (for example a hollow cube for which the DE is negated so it is turned inside out).

The "Baird Delta" (found in the same site as the "jerusalem cross") IS a KIFS ;D.
(Made with mandelbulber)

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 03, 2012, 04:43:53 PM

Wow excellent!!! I will certainly try to stick it (the JC3) inside a m3f using my assembly messing (some day) :D

Baird delta looks very cool, even if I have no idea about how you did that? :o :D )

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 03, 2012, 08:05:06 PM

Quote from: knighty on December 03, 2012, 03:14:55 PM

:embarrass:
Unfortunately, that's not true.

Code:

I wonder if you are also able to make a "general" version that calculate the limit, and the other scale, so that Scale1 is a user parameter.

Code:

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<100;i++){
      x=abs(x);y=abs(y);z=abs(z);
      if(x<y){t=x;x=y;y=t;}
      if(z<x){t=z;z=x;x=t;}
      if(x<y){t=x;x=y;y=t;}

      if(y<a && x>1-3*a+y){
         x-=1;z-=1;
         x*=scl1;y*=scl1;z*=scl1;dd*=scl1;
         x+=1;z+=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
}

I tried unsuccessfully to implement it. One reason can be the unusual folding style? Why you use

if(x<y){t=x;x=y;y=t;}
if(z<x){t=z;z=x;x=t;}
if(x<y){t=x;x=y;y=t;}

instead of the folding of normal menger;

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;}

And yes! It's very hard for me to change this part since it's a stack juggling. :'(

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: M Benesi on December 03, 2012, 08:41:54 PM

x-y<0 is the same as x<y

Switching x and y, when done in a different order, is the same operation.

x1=x;x=y;y=x1; // is the same as (t=x1)

x1=y;y=x;x=x1; // it's just done in a different order

Both of the variations order x,y, and z in terms of greatest value. The "normal" Menger orders variables x>y>z. Knighty's orders it y<x<z (z>x>y). You'd have to change the variables (in the if/else statement) below the ordering if you want to do the standard Menger ordering and maintain the formulas structure. Wonder what happens when you do it out of order?

@knighty- Nice implementation. I really want to learn to visualize these ideas a bit better. Didn't pick up on the scaling factor from alt.fractals website.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 04, 2012, 09:40:37 AM

Thanks I knew that was an order relationship in the old formula and I know diseq. rules too from primary schools :tease: :tease: :tease: ... Only, to make it in assembly is harder and I did not go deep in understanding :dink:

Will try again - I obtained a fractal with some crosses at some point yesterday but it was NOT a Menger still! :evil1:

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 04, 2012, 11:31:47 AM

I tried basically every possible combination ;D ;D ;D so finally I found the only correct one, yays

Obviously, zooming in reveals some awful noise but it's great :beer: thanks sir K! :dance:

(http://img15.imagefra.me/i5c4/kriptokapi/mc3p_4a4_u6bci.jpg) (http://i.imagefra.me/421jgvk9)Uploaded at ImageFra.me (http://imagefra.me/)

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: bib on December 04, 2012, 01:19:58 PM

Thanks knighty and Darkbeam!!

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty on December 04, 2012, 02:20:20 PM

Nicely done Darkbeam. I think there should not be any noise. Could you try this (its' the permutation (x,y,z)->(y,z,x)):

Code:

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<100;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
}

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

@Benessi & Darkbeam:
It's not very complicated to find a KIFS representation when We already have a picture of the fractal (and aobviousely when a KIFS representation is possible). Ok! Sometimes it's tricky and you usually need to do some geometry and algebra. It's much simpler to begin with 2D examples. That's what I usually do and that's what i did for the "Jerusalem cross".
Here is the code for the "Baird Delta" and the process. Notice that the code is a straightforward transcription of the process):

Code:

BD(x,y,z){
   r=x*x+y*y+z*z;dd=1;scl=1.5;
   for(i=0;i<MI && r<100;i++){
      //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;
      //y=abs(y);//not necessary
      
      //PI/2 rotation about x axis
      t=y;y=-z;z=t;
      
      //set (1,0,0) as origin
      x-=1;
      
      //scale
      x*=scl;y*=scl;z*=scl;dd*=scl;
      
      //Back to center
      x+=1;
      
      //norm squared
      r=x*x+y*y+z*z;
   }
   (sqrt(r)-1.)/dd
}

(Process in the attached picture)

There is also another version of the "Baird Delta" attached (fragmentarium script).

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty on December 04, 2012, 03:55:39 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.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam 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 :D ) but in normal circumstances it's not too disturbing :angel1:

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. :beer: It should work like my PolyFolding but it is slow due to a trig formula...

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 04, 2012, 04:22:55 PM

Quote from: knighty on December 04, 2012, 02:20:20 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. ^-^

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 ;D

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..
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...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD4ocyFE0ujz1..........2.28.kFrA0.
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zzzz.............0...................2./8.kzzzD............8....................
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...................................wz...................kz1........wz...........
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Title: Re: Jerusalem cube - can be made via KIFS?
Post by: bib on December 04, 2012, 05:03:47 PM

Quote from: knighty on December 04, 2012, 03:55:39 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

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: M Benesi on December 04, 2012, 07:42:25 PM

Quote from: knighty on December 04, 2012, 03:55:39 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. :D

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty on December 04, 2012, 07:55:29 PM

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

@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 :evil1:: When using multiple iterations the copies belonging to even iteration number are not hollow. :fiery:

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: David Makin 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).

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: bib 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.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: bib on December 05, 2012, 02:20:44 AM

(http://images1.sw-cdn.net/model/picture/674x501_813222_689476_1354668376.jpg)
http://www.shapeways.com/model/813222/jerusalem-cube-4cm.html

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty on December 05, 2012, 10:40:02 AM

:-\ 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
}

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam 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

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: David Makin 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 (http://speedtest.net/result/2298282143.png)

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: M Benesi 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.

(https://lh3.googleusercontent.com/-RBxy-Ey_qVQ/UMF2a3sasFI/AAAAAAAAB4M/VNJznS1M5Eg/s800/Jerusalem-2.jpg)

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);
}

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty 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.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty 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.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: M Benesi on December 07, 2012, 08:37:22 PM

Quote from: knighty 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.

The author's Jerusalem Cross (http://alt-fractals.blogspot.it/search/label/Jerusalem%20Cross) look like he only targets specific sizes of cross each iteration. Might be fun figuring out how to do that.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: David Makin on December 08, 2012, 12:52:39 PM

Quote from: knighty on December 07, 2012, 08:05:33 PM

Have you managed to get the Hart+DE method to work with non-affine transforms ?

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty on December 08, 2012, 03:08:11 PM

Not yet but I believe it's possible.

@M Benessi: See the attached fragmentarium script. O0

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: M Benesi on December 10, 2012, 07:47:04 AM

DOH!@!#!@$

Thanks Knighty. :D hahahhaa... that cracked me up. Still grinnin.

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: DarkBeam on December 10, 2012, 11:38:26 AM

I modded your formula this way;

Code:

JC4(x,y,z,alpha,beta){
   t=beta-1;
   scl=(alpha+t);
   scl1=scl/alpha;
   a=1/scl1;
   r=x*x+y*y+z*z;dd=1;
   for(i=0;i<MI && r<100;i++){
      x=abs(x);y=abs(y);z=abs(z);
      if(x<y){t=x;x=y;y=t;}
      if(z<x){t=z;z=x;x=t;}
      if(x<y){t=x;x=y;y=t;}

      if(y<a && x>1-beta*a+y){
         x-=1;z-=1;
         x*=scl1;y*=scl1;z*=scl1;dd*=scl1;
         x+=1;z+=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
}

It is nice but even more discontinue :embarrass:

Title: Re: Jerusalem cube - can be made via KIFS?
Post by: knighty on December 10, 2012, 08:02:08 PM

It is always difficult to get continuous DE when the transform contains 'if' statments (if not possible at all). :hurt:

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Fractal Math, Chaos Theory & Research => Sierpinski Gasket => Topic started by: DarkBeam on November 30, 2012, 07:06:34 PM