POVRAY produced images and simulation regarding paper by R. Gilmore, Two-parameter families of strange attractors, Chaos 17, 013104 (2007). van der Pol

Simulation and images by Timothy Jones

k = -2


k = -1


k = 0


k = 1


k = 2



all.ini

Output_File_Type=N
Width=600
Height=400
Quality=11
Antialias=on
Antialias_Threshold=0.001
Initial_Frame=1
Final_Frame=500
Initial_Clock=0
Final_Clock=1

// camera-----------------------------------------------------------

#declare Cam1 =camera {location  < 4.5*(1-clock) , 0 ,2+clock*10 >
                       look_at   < 0 , 0.0 , 2 >
                       }

camera{Cam1}                                             
light_source{< 1000, 100, -200 > color White*0.5}


background {
   color rgb <1,1,1>
}

#macro SP(x0,y0,z0,r0)
    sphere { < y0,x0,z0 >  , r0
               pigment {  rgb < 0.5-0.5*y0/0.4,0.6,0 >}
               finish { reflection .5 phong .7 }} 
#end

#!/usr/bin/perl
#for($num=0; $num<=1000; $num+=100){
#system("./torus $num");
#$number=$num+1000;
$file="new".".pov";
system("cat temp.pov > $file");
#system("cat $num >> $file"); 
system("cat donut.dat >> $file");
system("povray all.ini $file ");#Display=False");}

#include 
#include 
#include  
#include 
#include 

//Adaptation of a Bob Gilmore program
//written in f

int main(int argc, char *argv[]){
  nn=350000;
  double pi,r1,r2;
  double phi,alpha,beta,theta;
  double u,v,z,r,x,xx,y,yy,angle,oldang,origx,origy,origz;
  double uu,zz,aa,bb;
  double delu,delv,rat;

  ///////////////////////////////////PART ONE//////////////

  pi = 3.1415926535;
  alpha = 1.0/12.52;//  !!! 1.0/25.1
  aa = 0.45;   //!!!  0.85
  bb = sqrt(1.0-aa*aa);
  r1 = 1.0;
 
  double X,Y,t;
  double DX,DY;
  double PI=3.14159265;
  double A,b,c,d,w,T,dt;
  int k=-2;
  A = 0.25;
  b = 0.7;
  c=1.0;
  d=10.0;
  T=4.0;
  w=2*PI/T;
  int FLAG=0;
  X=0;
  Y=-1;
  dt=0.001;
  t=0;

  FILE * fp;
  fp  = fopen ("donut.dat","w");
 for(i=1; i<=nn;i++){    //    !!!  nn/1000= numbor of wraps in long. dir.
    DX=b*Y + (c-d*Y*Y)*X;
    DY=-X+A*sin(w*t);
    X += DX * dt;
    Y += DY * dt;
    t += dt;
    if(t>T){t=0;}

    xx=  ((cos(k*w*t)*X-sin(k*w*t)*Y));//  
    yy=  ((sin(k*w*t)*X+cos(k*w*t)*Y));//v;

    origx=  cos(w*t)*(3 + (cos(k*w*t)*X-sin(k*w*t)*Y));// 
    origy=   sin(w*t)*(3+(cos(k*w*t)*X-sin(k*w*t)*Y));//v;
    origz= sin(k*w*t)*X+cos(k*w*t)*Y;// z; 
    fprintf(fp, "SP((1-clock)*%f + clock*%f,(1-clock)*%f + clock*%f , (1-clock)*%f + clock*(%f), 0.02) \n",xx,origx,yy,origy,t,origz);}

  fclose(fp);
}

 mencoder "mf://*.png" -mf fps=25 -o test.flv -of lavf -ovc lavc -lavcopts vcodec=flv:vbitrate=14400:vhq -lavfopts i_certify_that_my_video_stream_does_not_use_b
_frames

flvtool2 -U [flvfile]

mencoder "mf://*.png" -mf fps=25 -o test.avi -ovc lavc -lavcopts vcodec=msmpeg4:vbitrate=14400:vhq