Summary

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Summary

What happens here ?

• number n grows from 0 to infinity (See : for (n=1; n<1000000 )
• rotation number t grows from 0.38 to 0.5
• on parameter plane : point c moves along boundary of main cardioid toward c=0.75 ( root point of period 2 component of Mandelbrot set)
• on dynamic plane there is a sequence of Siegel discs which ends at parabolic flower ( two sepals)
  • Points
    • 2 points of period=2 cycle moves toward :
      • critical orbit
      • fixed point alpha
      • themselves
    • For n= infinity these 5 points coincidies ( gluing ). It is parabolic fixed point with external rays 1/3 and 2/3
    • fixed point alpha moves toward z=-1/2
  • Curves : simple closed curve ( non-self intersecting) is glued. Then there are 2 curves sharing one common points.

Compare with

• Mandelbrot Set - Convergent Evolution of P/Q Limbs in Seahorse Valley by izaytsev ( similar effect on the parameter plane )

to do

• add final image : c= -3/4 ( root point ) with 4 mainn chessboard boxes
• add period 2 cycle with external ray that land on it ( 1/3 and 2/3)
• add fixed point

C src code

/*

  program in c language
  for console
  it uses qd library ( libqd) for quad double precision

  --------- description --------------
  https://commons.wikimedia.org/wiki/File:InfoldingSiegelDisk1over3.gif
  https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/siegel#1.2F3

  program draws series of images 
  of critical orbit 
  for complex quadratic polynomial
  fc(z) = z^2 + c
  where parameter c is computed from integer n 
  near t=1/2

  c = c(n) = c(t(n))
  -----------------------------
 to change t change : 
 - GiveT
 - some code in BackwardOrbit which chooses good preimage. 
   It is specyfic to t. Here see lines : 443-445

  ------- compile and run ---------------
  gcc c.c -lqd -Wall -DUSE_QD_REAL
  ./a.out

  ---------- git ------------------

  cd existing_folder
  git init
  git remote add origin git@gitlab.com:adammajewski/InfoldingSiegelDisk_in_c_1over2_quaddouble.git
  git add c.c
  git commit -m " first commit"
  git push -u origin master

*/

#include <stdio.h>
#include <stdlib.h> // malloc
#include <string.h> // strcat
#include <math.h>
#include <qd/c_qd.h> // qd library :  quad double number with precision = 64 decimal digits

// virtual 2D array = rectangle = matrix 
unsigned int iWidth = 1000;
unsigned int  iHeight = 1000;

// memmory 1D array 
unsigned char *data;
unsigned int  iLength; // = langth ( data)

/* colors */
const unsigned int MaxColorComponentValue=255; /* color component is coded from 0 to 255 ;  it is 8 bit color file */
const int iExterior = 0; /* exterior of Julia set */
const int iBoundary = 255; /* border , boundary, Julia set */

/* world coordinate */
 double ZxMin = -1.0;
 double ZxMax =  0.1;
 double ZyMin = -0.45;
 double ZyMax =  0.65;

 
double PixelWidth ;
double PixelHeight ;
double invPixelWidth ;
double invPixelHeight ;

// n -> t -> c =cx+cy*i
int n;
double t[4];
double cx[4];
double cy[4];

// number of iterations 
unsigned long long int iMaxForward;
unsigned long long int iMaxBackward;

// ------------- functions -------------------------------------

/* phi = (1+sqrt(5))/2 = golden ratio
 https://en.wikipedia.org/wiki/Golden_ratio

input = none
output = p

*/
void GivePhi(double p[4]){

  double a[4];

  c_qd_copy_d(5.0, p); // p = 5.0
  c_qd_copy_d(1.0, a); // a = 1.0

  c_qd_sqrt(p, p); // p = sqrt(p) =sqrt(5)
  c_qd_add(p, a, p); // p= a+p = 1+sqrt(5)
  c_qd_selfmul_d(0.5, p); // p = p*0.5 = p/2 = phi
  
  
}

/*

  compute floating point number from continued fraction
  t(n) = [0;2,10^n,phi]

  = 1/ (2 + (1 /(n + (1/phi))))

input n > 0 !!!
output t

*/

void GiveT(int n,  double t[4]){

  double p[4], a[4], b[4], one[4],  two[4];

  double phi[4];

  
  //
  c_qd_copy_d(1.0, one); // one = 1.0
  c_qd_copy_d(2.0, two); // two = 2.0
  c_qd_copy_d(10.0, a); // a = 10.0
  // a
  //c_qd_npwr(a, n, p); // p = a^n
  c_qd_copy_d((double) n, p); // p = n

  GivePhi(phi); 
  c_qd_div(one,phi,b); // b= one/phi = 1/phi
  
  c_qd_add(p,b,t); // t= p+b = p+1/phi = (a^n) +1/phi
 
  c_qd_copy(one,b);
  c_qd_selfdiv(t,b); //b= 1/t
 
  c_qd_add(two, b, t); // t = 2+b

  c_qd_copy(one,b);
  c_qd_selfdiv(t,one); //t= 1/b

  c_qd_copy(one,t);

}

/* 
   compute complex number c = point on the boundary of period 1 component of Mandelbrot set 
  
   double a = t *2*M_PI; // from turns to radians
   double cx, cy; 
   // c = cx+cy*i 
   cx = (cos(a))/2-(cos(2a))/4; 
   cy = (sin(a))/2-(sin(2a))/4;

   input t
   output cx,cy  where c = cx + cy*I

*/
void GiveC( double t[4], double cx[4], double cy[4]){
  double  a[4];
  double a2[4];
  double  p[4];
  // 
  double   s[4];
  double  s2[4];

  c_qd_pi(p);
  
  c_qd_selfmul_d(2.0,p); // p = 2 *pi
  c_qd_mul(t, p,  a);

  c_qd_mul_qd_d(a, 2.0, a2); // a2 = 2*t*p
  //
  c_qd_cos(a,s);   // s  = cos(a)
  c_qd_cos(a2,s2); // s2 = cos(a2)
  //
  c_qd_selfdiv_d(2.0,s);   // s  = s/2
  c_qd_selfdiv_d(4.0,s2);  // s2 = s/4 
  //
  c_qd_sub(s,s2,cx); // cx = s - s2

  //

  c_qd_sin(a,s);   // s  = sin(a)
  c_qd_sin(a2,s2); // s2 = sin(a2)
  //
  c_qd_selfdiv_d(2.0,s);   // s  = s/2
  c_qd_selfdiv_d(4.0,s2);  // s2 = s/4 
  //
  c_qd_sub(s,s2,cy); // cy = s - s2

}

 int DrawPoint( double Zx[4], double Zy[4], unsigned char A[])
{
  unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
  unsigned int i; /* index of 1D array  */

 // if (Zx[0] < ZxMin || ZxMax  < Zx[0] || Zy[0] < ZyMin || ZyMax < Zy[0]) {  printf("   point z = %f , %f out of bounds  \n", Zx[0], Zy[0]); return -1; }

  
  iX = (int)((Zx[0]-ZxMin)*invPixelWidth);
  iY = (int)((ZyMax-Zy[0])*invPixelHeight); // reverse Y axis
  i = iX + iY*iWidth;//f(iX,iY);
  
  
  A[i] = iBoundary;  /* draw */
  return 0;
}

/*

  forward iteration without explicit use of complex number 
  f(z) = z^2 + c = complex quadratic polynomial
  -----------------
  tmp = 2 * zx * zy + cy;
  zx= zx2 - zy2 + cx;
  zy = tmp;

  input: 
    z0 = z0x + z0y*i
    iMaxF

*/

int ForwardOrbit(const double z0x[4], const double z0y[4], unsigned long long int iMaxF){

  
  unsigned long long int i; // iteration number
  double tmp[4];
  
  double zx[4];
  double zy[4];
  double zx2[4];
  double zy2[4];

   c_qd_copy(z0x, zx);
   c_qd_copy(z0y, zy);

 
  for (i=0; i<iMaxF; i++) {
    
    // manual debug
    //printf("i = %llu \n", i);
    //printf("zx = "); c_qd_write(zx); 
    //printf("zy = "); c_qd_write(zy);

    // tmp = 2 * zx * zy + cy;
    c_qd_mul_qd_d(zx, 2.0, tmp); // tmp = 2*zx
    c_qd_selfmul(zy, tmp);   // temp  = temp*zy = 2*zx*zy
    c_qd_selfadd(cy, tmp);   // temp  = temp+cy = 2*zx*zy +cy
    // zx= zx2 - zy2 + cx;
    c_qd_sqr(zx, zx2); // zx2 = zx*zx
    c_qd_sqr(zy, zy2); // zy2 = zy*zy
    c_qd_sub(zx2,zy2, zx); // zx = zx2-zy2
    c_qd_selfadd(cx, zx);   // zx  <- zx + cx = zx2-zy2 +cx
    // zy = tmp;
     c_qd_copy(tmp, zy); 
   // no escape ( bailout ) test !!
    
    DrawPoint(zx, zy, data);

  }

  return 0;
}

/*

  backward iteration without explicit use of complex number 
  f^(-1)(z) = sqrt(z- c) 
   ------- subtraction ------
   b  = z  - c = bx + by*i
   bx = zx - cx
   by = zy - cy 
  ---------- principal value of complex square -----
   For every non-zero complex number z 
   there exist precisely two numbers w such that 
   w2 = b
  
   - the principal square root of z (defined below) :  w= sqrt(b)
   - its negative : -w = sqrt(b)

   w = sqrt(b)  = wx + wy*i
   r = abs(b) = sqrt(bx*bx + by*by)
   wx = sqrt((r+bx)/2)
   wy = sqrt((r-bx)/2)

   the sign of the wy is :
     - the same as the sign of by, 
     - positive when zero
  -------------  choose good preimage ----------------------
  
  ---------------- 
   z = f^(-1)(z ) = sqrt(z-c)
   z=w

*/

int BackwardOrbit(const double z0x[4], const double z0y[4], unsigned long long int iMaxB){

   double  zx[4];
   double  zy[4];

   // b 
   double  bx[4];
   double  by[4];
   double  bx2[4]; // bx2 = bx*bx
   double  by2[4];
   double  r[4]; // r = abs(b)

   double  tmp[4];

   c_qd_copy(z0x, zx);
   c_qd_copy(z0y, zy);

   unsigned long long int i; // iteration number
    
    for (i=0; i<iMaxB; i++) {

      //--- manual debug ----------
      //printf("i = %llu \n", i );
      //printf("zx = "); c_qd_write(zx); 
      //printf("zy = "); c_qd_write(zy);

      // -------- b = z - c ---------
      c_qd_sub(zx, cx, bx); // bx = zx - cx
      c_qd_sub(zy, cy, by); // by = zy - cy

      
     // -------- z = sqrt(b) --------------
     c_qd_sqr(bx, bx2); // bx2 = bx*bx
     c_qd_sqr(by, by2); // by2 = by*by
     c_qd_add(bx2, by2, r);   // r = bx2 + by2 
     c_qd_sqrt(r,r); // r = sqrt(r)
    
      // zx
     c_qd_add(r,bx, tmp);   // tmp = r + bx
     c_qd_selfdiv_d(2.0, tmp); // tmp = tmp/2.0
     c_qd_sqrt(tmp,zx); // zx = sqrt(tmp)
     
     // zy
     c_qd_sub(r,bx, tmp);   // tmp = r - bx
     c_qd_selfdiv_d(2.0, tmp); // tmp = tmp/2.0
     c_qd_sqrt(tmp,zy); // zy = sqrt(tmp)

     
     // the sign of the wy is  the same as the sign of by, 
     if (by[0]<0.0 ) 
             c_qd_neg(zy,zy); //zy = -zy

     //-------------  choose good preimage here A -----------
     // https://en.wikibooks.org/wiki/Fractals/mandel#complex_quadratic_polynomial
     // aproximation of rays landing on the critical point by line y = f(x) = x  
     if (zy[0]/zx[0]<1.0){
     c_qd_neg(zx,zx); //zx = -zx
     c_qd_neg(zy,zy); //zy = -zy 
     }
    //

    DrawPoint(zx, zy, data); 
     
   }

  return 0;
}

int CriticalOrbit(unsigned long long int iMax_F, unsigned long long int iMax_B){

  
  double  z0x[4];
  double  z0y[4];
  
  // critical point z = zx+zy*i = 0
  c_qd_copy_d(0.0, z0x); // zx= = 0.0
  c_qd_copy_d(0.0, z0y); // zy = 0.0

  ForwardOrbit( z0x,z0y, iMax_F); // forward iteration of critical point 
  BackwardOrbit(z0x,z0y, iMax_B); // backward iteration of critical point

  return 0;
}

unsigned long long int Give_iMaxForward( int n){
   
  if (n <       100) return     1000000;
  if (n <      1000) return    10000000;
  if (n <     10000) return    10000000;
  if (n <    100000) return   100000000;
  if (n <   1000000) return  1000000000;
  if (n <  10000000) return 10000000000;
  
                    return      100000;
 
}

unsigned long long int Give_iMaxBackward( int n){
   
  if (n <       100) return     100;
  if (n <      1000) return    1000;
  if (n <     10000) return    1000;
  if (n <    100000) return    1000;
  if (n <   1000000) return    1000;
  if (n <  10000000) return    1000;
  
                    return     1000;
 
}

// prints out important informations
void info(int n_){

  printf("\n\n ------------------------------------------ \n\n");
  printf("n = %d \n", n_ );
  printf("t = "); c_qd_write(t); 
  printf("cx = "); c_qd_write(cx); 
  printf("cy = "); c_qd_write(cy);  
  printf("iMaxForward = %llu\n", iMaxForward );
  printf("iMaxBackward = %llu\n", iMaxBackward );
  printf("\n\n");

}

int ClearArray( unsigned char A[] )
{
  int i; /* index of 1D array  */
  for(i=0;i<iLength;++i)  A[i]=iExterior;
  return 0;
}

// save data array to pgm file 
int SaveArray2PGMFile( unsigned char A[], double k, char* comment )
{
  
  FILE * fp;
  const unsigned int MaxColorComponentValue=255; /* color component is coded from 0 to 255 ;  it is 8 bit color file */
  char name [100]; /* name of file */
  snprintf(name, sizeof name, "%.0f", k); /*  */
  char *filename =strncat(name,".pgm", 4);
  
  
  
  /* save image to the pgm file  */      
  fp= fopen(filename,"wb"); /*create new file,give it a name and open it in binary mode  */
  fprintf(fp,"P5\n # %s\n %u %u\n %u\n", comment, iWidth, iHeight, MaxColorComponentValue);  /*write header to the file*/
  fwrite(A,iLength,1,fp);  /*write image data bytes to the file in one step */
  
  //
  printf("File %s saved. \n", filename);
  //if (comment == NULL)  printf ("empty comment \n");
  //                 else printf (" comment = %s \n", comment); 
  fclose(fp);

  return 0;
}

void MakeImage(int _n){

  // n -> t
  GiveT(_n,t); // continued fraction
  
  // t -> c
  GiveC(t, cx,cy);

  ClearArray(data);

  // c -> critical orbit 
  iMaxForward   = Give_iMaxForward(_n);
  iMaxBackward  = Give_iMaxBackward(_n);
  
  info(_n);

  CriticalOrbit(iMaxForward, iMaxBackward);
  SaveArray2PGMFile(data, _n, "test");

}

int Step(int n){

if (n <    10) return     1;
if (n <    20) return     2;
if (n <    30) return     4;
if (n <    50) return     5;
if (n <    70) return     7;
if (n <   100) return    10;
if (n <   150) return    15;
if (n <   300) return    30;
if (n <   500) return    50;
if (n <   700) return   100;
if (n <  1000) return   300;
if (n <  3000) return   500;
if (n <  6000) return   800;
if (n <  8000) return  1000;
if (n < 10000) return  3000;
if (n < 30000) return  6000;
if (n < 60000) return  9000;
if (n < 90000) return 12000;
               return 30000;
}

// init = all procedures before start of main computations 
int setup(void){

  iLength = iWidth*iHeight; // size = number of points in array 
  
  //
  PixelWidth  =  ((ZxMax-ZxMin)/iWidth);
  PixelHeight =  ((ZyMax-ZyMin)/iHeight);
  invPixelWidth  = 1 / PixelWidth;
  invPixelHeight = 1 / PixelHeight;

 
  /* create dynamic 1D arrays for colors ( shades of gray ) */
  
  data = malloc( iLength * sizeof(unsigned char) );
  
  if (data == NULL )
    {
      fprintf(stderr," Could not allocate memory\n");
      return 1;
    }

  fpu_fix_start(NULL); // libqd : turns on the round-to-double bit in the FPU control word on Intel x86 Processors. 
  return 0;
}

// all procedures before end of the program
void terminate(void){

  //
  fpu_fix_end(NULL); // libqd : 
  
  free(data);

}

// ------------------------------------------------------------------------------------------------------------------------

int main(void) {

  setup();

  // n from 1 not 0 
  for (n=1; n<1000000; n=n+ Step(n))  
    MakeImage(n); // for t tending to 1/2
 
 
 
 
  terminate();

  return 0; 
}

Text output

 ------------------------------------------

n = 1 
t = 3.81966011250105151795413165634361882279690820194237137864551377e-01
cx = -3.90540870218400050669762600713798485817583715938583500790716491e-01
cy = 5.86787907346968751196714643055715840096745752123320842032245424e-01
iMaxForward = 1000000
iMaxBackward = 100

File 1.pgm saved.

 ------------------------------------------

n = 2 
t = 4.19821271704535895291326075851421647065482652709614805648677148e-01
cx = -5.71364841537069242992335483094541839777704105988912656260232074e-01
cy = 4.52751034742476702053088187015075976704083160633117701649227228e-01
iMaxForward = 1000000
iMaxBackward = 100

File 2.pgm saved.

 ------------------------------------------

n = 3 
t = 4.39291418991932091877567317237601229603880941284056866520498343e-01
cx = -6.44775266780152674340681687619073035033689210770332424567743461e-01
cy = 3.58882903503757938762210889750192743983099115616886727299910113e-01
iMaxForward = 1000000
iMaxBackward = 100

File 3.pgm saved.

 ------------------------------------------

n = 4 
t = 4.51153118453388048274654014141790476571530664064504455290431333e-01
cx = -6.80997488902764214227025613031441146173281883009279127943727113e-01
cy = 2.95059367969553650459324351105113055833293401726033736166334357e-01
iMaxForward = 1000000
iMaxBackward = 100

File 4.pgm saved.

 ------------------------------------------

n = 5 
t = 4.59137199881577840507416703519638295976003254524271188022478407e-01
cx = -7.01368370651898651427952441268742544565348765866383212428724996e-01
cy = 2.49775093189215331319579210453114354952223931957331955873911547e-01
iMaxForward = 1000000
iMaxBackward = 100

File 5.pgm saved.

 ------------------------------------------

n = 6 
t = 4.64877942365107157181327962837162864156261217120904768792341357e-01
cx = -7.13917819020785021720775150845331201651542156256290400705789621e-01
cy = 2.16237467443523959138251634414893896102912879184596377196819909e-01
iMaxForward = 1000000
iMaxBackward = 100

File 6.pgm saved.

 ------------------------------------------

n = 7 
t = 4.69204366433245522765469041017621141977593241779087763676101825e-01
cx = -7.22181490686720348294348171891857056451788651268146261167616049e-01
cy = 1.90495287387535811975888280992577324952788442745908182057791396e-01
iMaxForward = 1000000
iMaxBackward = 100

File 7.pgm saved.

 ------------------------------------------

n = 8 
t = 4.72581808720119102980894768264404932739921550517154433713687046e-01
cx = -7.27905912294997308778824871392914422118068878026778902554589216e-01
cy = 1.70153976061491198159523325765849843898818426892059486410190783e-01
iMaxForward = 1000000
iMaxBackward = 100

File 8.pgm saved.

 ------------------------------------------

n = 9 
t = 4.75291642597962052815688359982337423566521345391240635931459087e-01
cx = -7.32032329757717677201063217123642749237580855491792466918883956e-01
cy = 1.53694512271954789306627113289672088742845697135078800956652472e-01
iMaxForward = 1000000
iMaxBackward = 100

File 9.pgm saved.

 ------------------------------------------

n = 10 
t = 4.77514010098100999615707814770545919285367871341280412309203667e-01
cx = -7.35103725789203166246364354183070697092321099215970115885457098e-01
cy = 1.40112549815936743590686010452273467218741353649054870130630558e-01
iMaxForward = 1000000
iMaxBackward = 100

File 10.pgm saved.

 ------------------------------------------

n = 12 
t = 4.80942266179947276441689293930587807561681802416472439338240716e-01
cx = -7.39284642266385548795738357973902814784672867073522370816550012e-01
cy = 1.19029625842836600472417644197152201903695018732977084057783488e-01
iMaxForward = 1000000
iMaxBackward = 100

File 12.pgm saved.

 ------------------------------------------

n = 14 
t = 4.83463458265404229586912178221265260741617855173049759771675801e-01
cx = -7.41925080081509480782112425509188962778485139291424917337395474e-01
cy = 1.03435641237988587646837782432883933741895622235492657809555814e-01
iMaxForward = 1000000
iMaxBackward = 100

File 14.pgm saved.

 ------------------------------------------

n = 16 
t = 4.85395519125367904659670840858062451538489017840829992995226152e-01
cx = -7.43697991339406310797429519031821917240751333362417140412711759e-01
cy = 9.14411714110385377528922154279890814277315718764449239985753809e-02
iMaxForward = 1000000
iMaxBackward = 100

File 16.pgm saved.

 ------------------------------------------

n = 18 
t = 4.86923341586948020796440423574256884676777931200469219877719170e-01
cx = -7.44945460561885113476006761413016127092507138645956789504105827e-01
cy = 8.19322230932241439712639081731606057573512773721957976836621348e-02
iMaxForward = 1000000
iMaxBackward = 100

File 18.pgm saved.

 ------------------------------------------

n = 20 
t = 4.88161776795454479528654913375777829540890475974799851324222852e-01
cx = -7.45856251963884050322455826185353681164513103000745335348469964e-01
cy = 7.42104413803926313191931505635104270774997304208924076030570808e-02
iMaxForward = 1000000
iMaxBackward = 100

File 20.pgm saved.

 ------------------------------------------

n = 24 
t = 4.90046991730643712417661847252877615536198481591912032562912331e-01
cx = -7.47069747043581472582450210432362994817578857139868218251683777e-01
cy = 6.24347589929192863362285895771370937032332615102103558758740128e-02
iMaxForward = 1000000
iMaxBackward = 100

File 24.pgm saved.

 ------------------------------------------

n = 28 
t = 4.91414255505828775103227271425859354237534432826510943105121510e-01
cx = -7.47818973452292135092433216368792782854224078186412048264031038e-01
cy = 5.38804432844857324146877310335094972783067576081102739863107214e-02
iMaxForward = 1000000
iMaxBackward = 100

File 28.pgm saved.

 ------------------------------------------

n = 32 
t = 4.92451242725189414531460422105687029605895944556295713239338902e-01
cx = -7.48313727837304280010691052967081667446383989910506383832276501e-01
cy = 4.73857993016725858221015652232189618874385741550353636856095208e-02
iMaxForward = 1000000
iMaxBackward = 100

File 32.pgm saved.

 ------------------------------------------

n = 37 
t = 4.93441424600392961953610781728087303622321387165016589812124922e-01
cx = -7.48726920118007455694338408873363810128602236431769653607391704e-01
cy = 4.11795950581984366406867538868250133235456815893588129817704847e-02
iMaxForward = 1000000
iMaxBackward = 100

File 37.pgm saved.

 ------------------------------------------

n = 42 
t = 4.94201961989611387724890737035082348336082868980258936727008289e-01
cx = -7.49004963477270987837457235328790473238223379517049482139181293e-01
cy = 3.64100065839960486720142661015662284903004959340038430705130879e-02
iMaxForward = 1000000
iMaxBackward = 100

File 42.pgm saved.

 ------------------------------------------

n = 47 
t = 4.94804442757190566736293124995398668114338162063164507174967212e-01
cx = -7.49200958080507549101900445454205944388496496058225985065212139e-01
cy = 3.26301563379153829662908997384351456837354137277553067304804937e-02
iMaxForward = 1000000
iMaxBackward = 100

File 47.pgm saved.

 ------------------------------------------

n = 52 
t = 4.95293500507700480515049910908737918612313413114402531020454671e-01
cx = -7.49344274481057074731013595633994495227302772564336469715457397e-01
cy = 2.95610349326526727155651097403349597141080307692350337350590358e-02
iMaxForward = 1000000
iMaxBackward = 100

File 52.pgm saved.

 ------------------------------------------

n = 59 
t = 4.95841514044740993954178072191563017322919772194827628627209961e-01
cx = -7.49488062014902230190169284721271334481474718710745507689850398e-01
cy = 2.61211062310805656906000824716949215518182264825830083329381909e-02
iMaxForward = 1000000
iMaxBackward = 100

File 59.pgm saved.

 ------------------------------------------

n = 66 
t = 4.96275218668623336290728778163750251915593335391228300296350849e-01
cx = -7.49589263691451808246105836160308760291623615929507943819229757e-01
cy = 2.33981507310636554770919448236393661914433105717972786508777814e-02
iMaxForward = 1000000
iMaxBackward = 100

File 66.pgm saved.

 ------------------------------------------

n = 73 
t = 4.96627001735664675277941184685578604388237075180883382425138916e-01
cx = -7.49663174882803436669273260614283083642308311232586230598443176e-01
cy = 2.11892072192087759215981773711380507207915982232203833932190910e-02
iMaxForward = 1000000
iMaxBackward = 100

File 73.pgm saved.

 ------------------------------------------

n = 83 
t = 4.97027985698840328657696801816063505430573130165141220386270387e-01
cx = -7.49738492030019529527796857725240863719944620774125654872439507e-01
cy = 1.86710035553581851408306263158994090246997296372679450714328230e-02
iMaxForward = 1000000
iMaxBackward = 100

File 83.pgm saved.

 ------------------------------------------

n = 93 
t = 4.97343760920145410507016408511877819031474091792079031044553076e-01
cx = -7.49791106425488209506342628786552499982718651305352940813267298e-01
cy = 1.66877054495989134927729371923522739315689259908894430741519703e-02
iMaxForward = 1000000
iMaxBackward = 100

File 93.pgm saved.

 ------------------------------------------

n = 103 
t = 4.97598878979725905466479804549371111642848867789583223653982594e-01
cx = -7.49829303590013319680606164021874085827724483111389557901667454e-01
cy = 1.50852575984426985546506916631458910800035550313098535511965845e-02
iMaxForward = 10000000
iMaxBackward = 1000

File 103.pgm saved.

 ------------------------------------------

n = 118 
t = 4.97901241385300136374785954406176323609159833890212166469665394e-01
cx = -7.49869585132834560474245101592311821550217927926990055099401128e-01
cy = 1.31859338521209523517357510083183567231383197484904511176863760e-02
iMaxForward = 10000000
iMaxBackward = 1000

File 118.pgm saved.

 ------------------------------------------

n = 133 
t = 4.98135970290013567226586261492196091053380451289448993835594344e-01
cx = -7.49897124545466070222926978144130879089230367099418674918388044e-01
cy = 1.17113746997768381912421217958503206057876351819405432431081507e-02
iMaxForward = 10000000
iMaxBackward = 1000

File 133.pgm saved.

 ------------------------------------------

n = 148 
t = 4.98323475750633480896784702683845243612305764221157226408352096e-01
cx = -7.49916779823725235433302147677341984767586027375924338781247503e-01
cy = 1.05334255075057409484950618002600224336409333042262741297120111e-02
iMaxForward = 10000000
iMaxBackward = 1000

File 148.pgm saved.

 ------------------------------------------

n = 163 
t = 4.98476706100335462118999582076336588891774052273713484985199494e-01
cx = -7.49931296563650020137568391115032537208180032925408907646102645e-01
cy = 9.57077252951126966144106118911416972173910205600225899012280221e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 163.pgm saved.

 ------------------------------------------

n = 193 
t = 4.98712123779213173244344991219834524488846442464174384780705784e-01
cx = -7.49950890881383031290233668733192402520792845409847447352989504e-01
cy = 8.09174417494256273454841385583668680213873272616664072449227924e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 193.pgm saved.

 ------------------------------------------

n = 223 
t = 4.98884516361532292808583761515624403065279045951102783470306496e-01
cx = -7.49963158095216924428251927958561192626886523470058849283229779e-01
cy = 7.00864695306196786861381878161316527518473814425326814315986233e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 223.pgm saved.

 ------------------------------------------

n = 253 
t = 4.99016205201669914560534484444596027973634912605035350261734460e-01
cx = -7.49971343318586311630329027842135197944667396160683478246119653e-01
cy = 6.18126661217529387843823006003232804900158100141279017287643698e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 253.pgm saved.

 ------------------------------------------

n = 283 
t = 4.99120084014061919253719216068732002204200143933310043554919871e-01
cx = -7.49977075488125902351849607239661841558395370141323745189465928e-01
cy = 5.52860478190410787465345185132000831405250562215610409519047157e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 283.pgm saved.

 ------------------------------------------

n = 313 
t = 4.99204120830550742195386248502273364546286202115440555087929792e-01
cx = -7.49981245194647327239266143519956837013542909635308168074581958e-01
cy = 5.00060420014984955619131826176708468195832001997636050082488208e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 313.pgm saved.

 ------------------------------------------

n = 363 
t = 4.99313409453354007135373041937109735952305705131148945327787215e-01
cx = -7.49986042275607001089578026897868814303998609261267851354326144e-01
cy = 4.31394218286083885630686705034649580958251288102552775842683943e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 363.pgm saved.

 ------------------------------------------

n = 413 
t = 4.99396307382240707717092188568522428240563823332927540175182787e-01
cx = -7.49989209261496242228803762912882041983611656906027342067411498e-01
cy = 3.79308984677288863118348645704070903300662878006700648753905100e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 413.pgm saved.

 ------------------------------------------

n = 463 
t = 4.99461343921822137302425626740536257947053276797908973904496053e-01
cx = -7.49991409016479062887510298875844036791046951174655784669785602e-01
cy = 3.38445980269467571654616389688696532956052818380949368856049789e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 463.pgm saved.

 ------------------------------------------

n = 513 
t = 4.99513730343087963755863137283001398953821013696757871892416658e-01
cx = -7.49992998770279825026280131744161381324549603740977826251485985e-01
cy = 3.05531047973156911979690712511834034136333776260833822410131304e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 513.pgm saved.

 ------------------------------------------

n = 613 
t = 4.99592912133883728642790796034807647568290333796061400800668854e-01
cx = -7.49995093219786916753164280455893938784410643357876618374810084e-01
cy = 2.55780152655134616771093310512492758720699273465263408763614078e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 613.pgm saved.

 ------------------------------------------

n = 713 
t = 4.99649917817361914625213836138717673199233094698267054589350984e-01
cx = -7.49996371221240709533240982551813784047096279162432955155551897e-01
cy = 2.19962679182466649628577921285353544338531751335480247547490648e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 713.pgm saved.

 ------------------------------------------

n = 1013 
t = 4.99753480372480218242789301404871271202519695320082853354839434e-01
cx = -7.49998200616452044138687874813430779224788385623881227723128646e-01
cy = 1.54892695316534517065243128730574509377694162303939162775685040e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 1013.pgm saved.

 ------------------------------------------

n = 1513 
t = 4.99834887377081556156691466209371764655311708841475226724085875e-01
cx = -7.49999192799473961119798544060867886622946888409984122867069185e-01
cy = 1.03743274111954869897710061283927247286419463110088380787787688e-03
iMaxForward = 10000000
iMaxBackward = 1000

File 1513.pgm saved.

 ------------------------------------------

n = 2013 
t = 4.99875876192069587315014796992722868249847117034405831654110453e-01
cx = -7.49999543825383836420849742946395709187591558799097149341432880e-01
cy = 7.79892688611019268498027571727256922154780757207642583900569969e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 2013.pgm saved.

 ------------------------------------------

n = 2513 
t = 4.99900561550165819027327033576694552794663202743473433693145449e-01
cx = -7.49999707227926530582885342655589851968041628911424180807947531e-01
cy = 6.24790105343990225023024693423326966441415603796714992290590935e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 2513.pgm saved.

 ------------------------------------------

n = 3013 
t = 4.99917056997376721472646509660135834283248338308938491629075210e-01
cx = -7.49999796304949180015995201929305262866465035744430333081061175e-01
cy = 5.21146196440988603044611698937792322797384914658912750253984062e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 3013.pgm saved.

 ------------------------------------------

n = 3813 
t = 4.99934454047365033014376969860649741891719199258647158870045333e-01
cx = -7.49999872792493034277247994919058517421499138368764374249356913e-01
cy = 4.11837337436221785275506350996076205317585706259078596809221088e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 3813.pgm saved.

 ------------------------------------------

n = 4613 
t = 4.99945818464512949746536216361981140109460519374197350036431461e-01
cx = -7.49999913079222020108589294861408948398323181153379431485872819e-01
cy = 3.40432611253402888442124719797758000649841433407726921843914426e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 4613.pgm saved.

 ------------------------------------------

n = 5413 
t = 4.99953824427463429867283443719165086533503414113103489315176001e-01
cx = -7.49999936868578389173800940673096598945724277633332840954997899e-01
cy = 2.90129668736660906132913173665717964604535374171407952920305246e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 5413.pgm saved.

 ------------------------------------------

n = 6213 
t = 4.99959769029388788625856710767630988707894409520691011044309836e-01
cx = -7.49999952077218831788215295932349881132978620600182065460465893e-01
cy = 2.52778636708017234098827183299147989487621646032119649391323853e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 6213.pgm saved.

 ------------------------------------------

n = 7213 
t = 4.99965345729190714005970675907329726313311890165292764622725230e-01
cx = -7.49999964442229317161540798718643366944372144061405491902557021e-01
cy = 2.17739200878638886463939575383558968084087352786148450756087251e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 7213.pgm saved.

 ------------------------------------------

n = 8213 
t = 4.99969564596105687954679061241485731324504986336687317608996854e-01
cx = -7.49999972572947676635148287790844358027899738454933518922187391e-01
cy = 1.91231279652978695343629009649818545011326065662078340531537688e-04
iMaxForward = 10000000
iMaxBackward = 1000

File 8213.pgm saved.

 ------------------------------------------

n = 11213 
t = 4.99977706673031059804674017404433338723538457888741888369704111e-01
cx = -7.49999985284644127511032315951259718552172210472092193079048780e-01
cy = 1.40073103314270136505606297151548064091434255185496137490895854e-04
iMaxForward = 100000000
iMaxBackward = 1000

File 11213.pgm saved.

 ------------------------------------------

n = 17213 
t = 4.99985477036958478927503017216118585573446303061556342546570535e-01
cx = -7.49999993755014080445543473016093280725259100692953048619780301e-01
cy = 9.12504676826096457514322114935740504950023717838244593118227734e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 17213.pgm saved.

 ------------------------------------------

n = 23213 
t = 4.99989230691442424620013729492816437456113663802401500285405926e-01
cx = -7.49999996566028864657408903523314455895195779409222972104428721e-01
cy = 6.76655611683512441256313546943455217691193711204462608005614412e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 23213.pgm saved.

 ------------------------------------------

n = 29213 
t = 4.99991442493670041961984699456260768469979370253731120076097239e-01
cx = -7.49999997831719530848134089736896536719445595788839363011927915e-01
cy = 5.37683979737192244910120507556955722841614483069148262741111701e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 29213.pgm saved.

 ------------------------------------------

n = 35213 
t = 4.99992900574713849161022523466669115995211215077283409704760896e-01
cx = -7.49999998507661353035014680617172148391645872715329094894077847e-01
cy = 4.46070046103795400625587540866077522722616351132607455736103493e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 35213.pgm saved.

 ------------------------------------------

n = 44213 
t = 4.99994345697457816136351201028854024772157976880871182010469432e-01
cx = -7.49999999053372569906517967197963110900681228781085392748999680e-01
cy = 3.55270306367140239705525758025976808805911376520460241062024523e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 44213.pgm saved.

 ------------------------------------------

n = 53213 
t = 4.99995301998619232572715694651071135055761170422018352109087872e-01
cx = -7.49999999346497459599489693595055729364309836169868462728252571e-01
cy = 2.95184132380304434312820357180718417954618211174035174230651914e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 53213.pgm saved.

 ------------------------------------------

n = 62213 
t = 4.99995981619479626468874625947918557484131722595196461443168603e-01
cx = -7.49999999521895182523407486416317156325023126915019814746178318e-01
cy = 2.52482294375613538688818823296159825506006839244916869399850260e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 62213.pgm saved.

 ------------------------------------------

n = 74213 
t = 4.99996631368712277838649599648730036386459915129423436384722912e-01
cx = -7.49999999664008758778217029744792178748694237508920621737606417e-01
cy = 2.11657346083705001845746539393340617576929539872073378627482573e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 74213.pgm saved.

 ------------------------------------------

n = 86213 
t = 4.99997100242910314980180822786508546358022308002640437142455052e-01
cx = -7.49999999751031594493716837735398301298386492536713571252891353e-01
cy = 1.82197111377786813724749926014536785652583143223113505068249163e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 86213.pgm saved.

 ------------------------------------------

n = 98213 
t = 4.99997454541108708189647681150550500666608013388321765913503566e-01
cx = -7.49999999808153811456223292783596450793710153266475063433045227e-01
cy = 1.59935899040897267914423898010474213360248690462761639449282378e-05
iMaxForward = 100000000
iMaxBackward = 1000

File 98213.pgm saved.

 ------------------------------------------

n = 128213 
t = 4.99998050136725709671185812811888480041389297855060959899181803e-01
cx = -7.49999999887428275560683676387088986134372463440891970458165420e-01
cy = 1.22513522752638762376139173039056942858310465350953516677721704e-05
iMaxForward = 1000000000
iMaxBackward = 1000

File 128213.pgm saved.

 ------------------------------------------

n = 158213 
t = 4.99998419862885142189935265253238724719070060415514198419322130e-01
cx = -7.49999999926071729170572506928940289164816959811615342211586270e-01
cy = 9.92829430299596727815312466543554616429722105925127842277881302e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 158213.pgm saved.

 ------------------------------------------

n = 188213 
t = 4.99998671725571857188669182980937166968963400645367572090402779e-01
cx = -7.49999999947760787241035751042344705636056610887856873490898783e-01
cy = 8.34579437056706972763511601487101422422536320935759414712153688e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 188213.pgm saved.

 ------------------------------------------

n = 218213 
t = 4.99998854336271858174079824715501636350632027773097115333683571e-01
cx = -7.49999999961137089083085835048147920585752734025875094672663766e-01
cy = 7.19841750347389126970437070711711830770071764461030462625502927e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 218213.pgm saved.

 ------------------------------------------

n = 248213 
t = 4.99998992805074988656754816706026482958617736033815407398894596e-01
cx = -7.49999999969963587657856070668227110868089711147116955609590428e-01
cy = 6.32839235419151605117521551590194740769558392720884336241892423e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 248213.pgm saved.

 ------------------------------------------

n = 278213 
t = 4.99999101411525171206081387102640978946437402870548107543119122e-01
cx = -7.49999999976092030766072701998960598373332203667071195005489635e-01
cy = 5.64599790217020032605854681193046569783650889080926000768032523e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 278213.pgm saved.

 ------------------------------------------

n = 308213 
t = 4.99999188875572622436151012842258673029175284400272784754319504e-01
cx = -7.49999999980519685626450055503231910974691602091397981290313930e-01
cy = 5.09644508433800894432029898556704990287366979245834560331322110e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 308213.pgm saved.

 ------------------------------------------

n = 338213 
t = 4.99999260823287173138326592174476349605799515425685355540257006e-01
cx = -7.49999999983822271124132367702690472087781778046085705348653848e-01
cy = 4.64438426140129984886088250962247907951244818921849620689083381e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 338213.pgm saved.

 ------------------------------------------

n = 368213 
t = 4.99999321047217486312559898284481035782500497473897868933161652e-01
cx = -7.49999999986351021642969866743522182764861717850064229369241696e-01
cy = 4.26598614732635021458292066173598227808286881684635765188858606e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 368213.pgm saved.

 ------------------------------------------

n = 398213 
t = 4.99999372197045061416525716082650751434992052486391917682541336e-01
cx = -7.49999999988330084507716178496027110031320335967052347460339454e-01
cy = 3.94460230224846170749539132587216705074283089930860225899734396e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 398213.pgm saved.

 ------------------------------------------

n = 428213 
t = 4.99999416179921512637550710781588469433609017806227540950004298e-01
cx = -7.49999999989907957888243068764176940340005271753690185965156689e-01
cy = 3.66824973916766197825335685588846152598118815645147563881818491e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 428213.pgm saved.

 ------------------------------------------

n = 458213 
t = 4.99999454403541574299859457726417057558341057950210692809193503e-01
cx = -7.49999999991186181860155262240647202255393479174493296250730016e-01
cy = 3.42808365121279138344011088157510274831219002296893547251000570e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 458213.pgm saved.

 ------------------------------------------

n = 488213 
t = 4.99999487929597352210598801548647131966311457389435305481607347e-01
cx = -7.49999999992236092557125782259219388862260111775929623751042178e-01
cy = 3.21743323014424748463266938235723813767105422715632735494993684e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 488213.pgm saved.

 ------------------------------------------

n = 518213 
t = 4.99999517573930736478042095627669892132696005441861450065884903e-01
cx = -7.49999999993108995455696552838763894667780215158332783046421259e-01
cy = 3.03117239018535832917955848103589113915879687169953861031247119e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 518213.pgm saved.

 ------------------------------------------

n = 548213 
t = 4.99999543973801885014133096858246902122694925367627986738434158e-01
cx = -7.49999999993842554363531418611337536594658039585941572301171599e-01
cy = 2.86529710767524481642529605843569404091488541850695970896415304e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 548213.pgm saved.

 ------------------------------------------

n = 578213 
t = 4.99999567634216801838056240979727145702706831149746466840686537e-01
cx = -7.49999999994464923412064223109830871597766807892079020588167101e-01
cy = 2.71663433630953187600697874773443799958367898338304924670398902e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 578213.pgm saved.

 ------------------------------------------

n = 608213 
t = 4.99999588960544342330963871613157298750053333156552327725921213e-01
cx = -7.49999999994997489329473069197250988372721603634161031733700718e-01
cy = 2.58263706845218364322676232241807207027993537758816769877009772e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 608213.pgm saved.

 ------------------------------------------

n = 638213 
t = 4.99999608281934015934770302317315929212598216287597843649714775e-01
cx = -7.49999999995456733596015349584534894392574291988165461892343664e-01
cy = 2.46123719674167016130177660845793761658177298640155045959766181e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 638213.pgm saved.

 ------------------------------------------

n = 668213 
t = 4.99999625868425624488623135039860896922233759209206144352171502e-01
cx = -7.49999999995855523102495139359401193734095496510942774868684664e-01
cy = 2.35073801106276721097844241754354830442979141149636616472604415e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 668213.pgm saved.

 ------------------------------------------

n = 698213 
t = 4.99999641943648025991201449046499060612410147491037519056119688e-01
cx = -7.49999999996204021313805439158471927558625510021494897012555247e-01
cy = 2.24973440986067019447500046579777065078009395665932499546514573e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 698213.pgm saved.

 ------------------------------------------

n = 728213 
t = 4.99999656694379017338041898653836874195943501426842671803655757e-01
cx = -7.49999999996510342304699272947079551071644470868431586229991354e-01
cy = 2.15705283362624368830445664220087234732654239990206223081132286e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 728213.pgm saved.

 ------------------------------------------

n = 758213 
t = 4.99999670277835701295717863613702331429762639170791664739507153e-01
cx = -7.49999999996781027370935379217905806436680765999980620497937047e-01
cy = 2.07170545816936747808271805245890630763905752898664158224497938e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 758213.pgm saved.

 ------------------------------------------

n = 788213 
t = 4.99999682827299993604407342004878093595075457917506344353564295e-01
cx = -7.49999999997021397164554698359862031605141463556623638515324805e-01
cy = 1.99285484851536578653239565990826677030582126920033998889104429e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 788213.pgm saved.

 ------------------------------------------

n = 818213 
t = 4.99999694456506567373897819103291883371701355301926942417526569e-01
cx = -7.49999999997235815166496414587202287706513841647236375173089338e-01
cy = 1.91978638863725066339234098978703619692412569855117158189058859e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 818213.pgm saved.

 ------------------------------------------

n = 848213 
t = 4.99999705263099629305791384484263600279747574323300827851827400e-01
cx = -7.49999999997427887121412855212963120051567743136324295949888059e-01
cy = 1.85188656189015321025627114844332643590347250366038236242049540e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 848213.pgm saved.

 ------------------------------------------

n = 878213 
t = 4.99999715331381190202558879425901476171279106555870288905267825e-01
cx = -7.49999999997600613624262338608134207622887443764298764217272077e-01
cy = 1.78862568311844151954079680311942063735693608106139240631293264e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 878213.pgm saved.

 ------------------------------------------

n = 908213 
t = 4.99999724734514652585404685547156212492423418013173061870625291e-01
cx = -7.49999999997756508026269358389458266551552035175324550715351235e-01
cy = 1.72954405310637745767125721704249913639840016132768993940448804e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 908213.pgm saved.

 ------------------------------------------

n = 938213 
t = 4.99999733536305631521916475730834809410745159424093834844859290e-01
cx = -7.49999999997897688384679147813712495088646801253781832336153049e-01
cy = 1.67424076935085798344230763531903885837555352522552826079905100e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 938213.pgm saved.

 ------------------------------------------

n = 968213 
t = 4.99999741792651704316653005295199690532270505408869368221180598e-01
cx = -7.49999999998025949787089177955372276682298631258558002555958527e-01
cy = 1.62236461701546040690410817295069139821663416792415714574677150e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 968213.pgm saved.

 ------------------------------------------

n = 998213 
t = 4.99999749552730738388925087092991208588710921650939261328746043e-01
cx = -7.49999999998142821695550657989070072803546033673411205560910930e-01
cy = 1.57360660244618079442694675345995134323986171432698155422134580e-06
iMaxForward = 1000000000
iMaxBackward = 1000

File 998213.pgm saved. 

Bash and Image Magic src code

#!/bin/bash
 
# script file for BASH 
# which bash
# save this file as g.sh
# chmod +x g.sh
# ./g.sh
 
# for all pgm files in this directory
for file in *.pgm ; do
  # b is name of file without extension
  b=$(basename $file .pgm)
  # convert  using ImageMagic
  convert $file ${b}.pgm
  echo $file
done

# for all pgm files in this directory
for file in *.pgm ; do
  # b is name of file without extension
  b=$(basename $file .pgm)
  # convert  using ImageMagic
  convert $file -morphology Thicken ConvexHull ${b}.gif
  echo $file
done

 
# convert gif files to animated gif
convert -delay 5   -loop 0 %d.gif[1-998000] a5.gif
 
echo OK
# end

also :

 convert a5.gif -resize 600x600 a5_600.gif

references

1. ↑ InfoldingSiegelDisk.gif by Arnaud Chéritat