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Author Topic: littlewood fractal  (Read 1639 times)
Description: drawing littlewood fractal with python
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0x80
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« on: September 30, 2013, 09:55:24 AM »

Hi , i am a web developer ..
I was playing with Python data visualization patterns and i have implemented
littlewood fractal .



i am no fractal expert , in fact this is my first fractal drawing which made me interested in fractals .
so my question is , are there any other variations of this fractal that i can play with ?

ps. if you into that stuff , here is a source code : https://github.com/Alexander-0x80/Beauty-of-roots

« Last Edit: September 30, 2013, 09:58:39 AM by 0x80 » Logged
Tglad
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« Reply #1 on: September 30, 2013, 10:17:36 AM »

There's a discussion of the formula here: http://www.math.ucr.edu/home/baez/roots/  he calls it the Christensen set, and you can adjust the parameters n and d.
It has some similarities with this: http://blogs.ams.org/visualinsight/2013/09/01/algebraic-numbers/

and also has some visual similarities with some fractals I made here: https://sites.google.com/site/tomloweprojects/scale-symmetry/mobius-maps

It is a nice fractal isn't it
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knighty
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« Reply #2 on: September 30, 2013, 10:30:24 PM »

I also remember a thread here in fractalforums about that fractal. Unfortunately, I can't find it by now.
See also: LINK describing an escape time definition.
I've also written a DE for it in the hope that it's 3D generalisation would give good looking fractal... That was not the case.
Code:
//Use with evaldraw (http://advsys.net/ken/download.htm)
(x,y){
   static binit=1;
   static frm=-1,mx,my,mr2;
   if(frm<numframes){
      frm=numframes;
      mx=(mousx-0.5*xres)*0.005;
      my=(0.5*yres-mousy)*0.005;
      mr2=deifs(mx,my);mr2*=mr2;
   }
   if((x-mx)^2+(y-my)^2<mr2) return 0;
   deifs(x,y)^0.25
}
static maxiter=100,maxdepth=30;
static tcx=0,tcy=1,tcr=sqrt(1);//tcr=sqrt(tcx^2+tcy^2)//is this thing invariant, the same for any tcx and tcy?
enum {Npq=256};
deifs(x,y){
   r2=x*x+y*y;inverted=0;
   if(r2<1){r2=1/r2;x*=r2;y*=r2;inverted=1;}
   if(r2<1.75) return 0.04;
   
   trx=x;
   try=y;
   s=sqrt(r2);r2=s;
   bvr=tcr/(s-1);//bvr=min(bvr,3);
   tis=1/s;
   
   //priority queue... the most stupid possible :o))
   auto pqx[Npq];//x
   auto pqy[Npq];//y
   auto pqs[Npq];//1/accumulated_scale
   auto pqd[Npq];//distance
   auto pqh[Npq];//depth
   stptr=0;//pointer in the priority queue
   
   bvrm=100;//controls the smoothness of the DE field (lower values faster, higher values smoother)
   
   {//first instances
      x0=tcx;y0=tcy;//initial value, faster than beginning at (0,0)
      pqx[stptr]=x0; pqy[stptr]=y0;
      pqs[stptr]=tis;//instead of 1 because of the initial value of (1,0)
      pqd[stptr]=tcr-bvr;
      pqh[stptr]=0;
      stptr++;
   }
   bNoExit=1;i=0;ii=0;
   while(bNoExit && i<maxiter){
      //extract nearest element
      {
         depth=pqh[stptr-1];
         if(depth>maxdepth) break;
         stptr--;
         x=pqx[stptr]; y=pqy[stptr];s=pqs[stptr];ad=pqd[stptr];
         
      }
      //generate and insert its children
      nx=x*trx-y*try;
      ny=x*try+y*trx;
      nc=-1;
      for(j=0;j<2;j++){
         //generate child j
         pqx[stptr]=nx+nc*tcx;
         pqy[stptr]=ny+nc*tcy;
         pqs[stptr]=s*tis;
         pqd[stptr]=(sqrt((pqx[stptr])^2+(pqy[stptr])^2)-bvr)*pqs[stptr];
         pqh[stptr]=depth+1;     
         nc=1;
         //insert it at its place
         ptr=stptr;
         imm=0;
         while(ptr>0){
            if(pqd[ptr]>pqd[ptr-1]){//swap
               k=pqx[ptr]; pqx[ptr]=pqx[ptr-1]; pqx[ptr-1]=k;
               k=pqy[ptr]; pqy[ptr]=pqy[ptr-1]; pqy[ptr-1]=k;
               k=pqs[ptr]; pqs[ptr]=pqs[ptr-1]; pqs[ptr-1]=k;
               k=pqd[ptr]; pqd[ptr]=pqd[ptr-1]; pqd[ptr-1]=k;
               k=pqh[ptr]; pqh[ptr]=pqh[ptr-1]; pqh[ptr-1]=k;
               ptr--;imm++;
            } else break;
         }
         stptr++;
      }
      d=pqd[stptr-1];x=pqx[stptr-1];y=pqy[stptr-1];s=pqs[stptr-1];
      bNoExit=(x*x+y*y<bvrm*bvr*bvr);
      i++;
   }
   DE=0.5*pqd[stptr-1]/bvr;
   if(inverted)
      return DE;//good for the interior!
   return r2^2/(1/DE+r2);//deduced from the interior distance
}


* JonesPolyFractal.jpg (47.84 KB, 640x484 - viewed 614 times.)
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Nahee_Enterprises
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« Reply #3 on: October 01, 2013, 12:38:11 PM »

    Hi , i am a web developer ..
    I was playing with Python data visualization patterns and i have implemented littlewood fractal .
            http://fc09.deviantart.net/fs71/f/2013/271/c/e/beauty_of_roots_by_rootdiver-d6oa1s5.png
    i am no fractal expert , in fact this is my first fractal drawing which made me interested in fractals .
    so my question is , are there any other variations of this fractal that i can play with ?
    ps.  if you into that stuff , here is a source code : https://github.com/Alexander-0x80/Beauty-of-roots

Greetings, and welcome to this particular forum !!!     cheesy

You have already gotten some good answers, and there are many ways to create visually similar fractal type images, if that is what you are trying for.
 
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0x80
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Posts: 2


« Reply #4 on: October 03, 2013, 02:21:01 PM »

Thank you for your replies ,thats fascinating ..

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