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Author Topic: Jerusalem cube - can be made via KIFS?  (Read 6303 times)
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #15 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
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cKleinhuis
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« Reply #16 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 .... wink
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Alef
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« Reply #17 on: December 03, 2012, 10:46:25 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. wink Even if it will not support rotates it will be surely appreciated from the MB3D folks!!! A Beer Cup A Beer Cup A Beer Cup
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.
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #18 on: December 03, 2012, 11:00:51 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 .... wink

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. wink
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #19 on: December 03, 2012, 12:27:52 PM »

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.

Hey, just scale (the other scale is automatic), cx,cy,cz, plus cx2,cy2,cz2, is not that much wink
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kram1032
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« Reply #20 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...
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knighty
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« Reply #21 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  grin.
(Made with mandelbulber)


* The Baird Delta.jpg (84.03 KB, 800x600 - viewed 484 times.)
* The Baird Delta.fract (8.35 KB - downloaded 205 times.)
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #22 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) cheesy

Baird delta looks very cool, even if I have no idea about how you did that? shocked cheesy )
« Last Edit: December 03, 2012, 04:47:01 PM by DarkBeam » Logged

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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #23 on: December 03, 2012, 08:05:06 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
}
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  grin.
(Made with mandelbulber)

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. cry
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M Benesi
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« Reply #24 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.  
« Last Edit: December 03, 2012, 09:12:29 PM by M Benesi » Logged

DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #25 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 wink

Will try again - I obtained a fractal with some crosses at some point yesterday but it was NOT a Menger still! evil
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #26 on: December 04, 2012, 11:31:47 AM »

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

Obviously, zooming in reveals some awful noise but it's great A Beer Cup thanks sir K! dance moves

Uploaded at ImageFra.me
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bib
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« Reply #27 on: December 04, 2012, 01:19:58 PM »

Thanks knighty and Darkbeam!!
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knighty
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« Reply #28 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).


* BD-process01.jpg (85.2 KB, 639x1440 - viewed 585 times.)
* Baird-Delta04.frag (2.35 KB - downloaded 197 times.)
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knighty
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« Reply #29 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.
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