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Summary
DescriptionInfoldingSiegelDisk1over2.gif |
English: Numerical approximation of critical orbit (Infolding Siegel Disk) for c near internal angle t=1/2 on the boundary of main cardioid of Mandelbrot set |
Date | |
Source | I have made it with significant help of Claude Heiland-Allen and Wolf Jung. This image is based on the idea taken from image by Arnaud Chéritat[1]. |
Author | Adam majewski |
Other versions |
|
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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
- 2 points of period=2 cycle moves toward :
- Curves : simple closed curve ( non-self intersecting) is glued. Then there are 2 curves sharing one common points.
- Points
Compare with
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
Captions
Critical orbit (Infolding Siegel Disk) for c near internal angle t=1/2 on the boundary of main cardioid of Mandelbrot set
Items portrayed in this file
depicts
some value
14 January 2017
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 11:45, 14 January 2017 | ![]() | 600 × 600 (632 KB) | Soul windsurfer | smaller size because Animated GIF files exceeding the 50 MP limit |
11:23, 14 January 2017 | ![]() | 1,000 × 1,000 (414 KB) | Soul windsurfer | User created page with UploadWizard |
File usage
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Metadata
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
GIF file comment | test
|
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Retrieved from "https://en.wikipedia.org/wiki/File:InfoldingSiegelDisk1over2.gif"