File:Mandelbrot set - real slice chotic band 2.png
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Summary
DescriptionMandelbrot set - real slice chotic band 2.png |
English: Mandelbrot set - real slice chotic band 2 |
Date | |
Source | Own work |
Author | Adam majewski |
Other versions |
|
c source code
/*
G. Pastor, M. Romera and F. Montoya, “An Approach to the Ordering of One-Dimensional Quadratic Maps,” Chaos, Solitons & Fractals, Vol. 7, No. 4, 1996, pp. 565-584. doi:10.1016/0960-0779(95)00071-2
https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Parameter_plane#Plane_types
Adam Majewski
adammaj1 aaattt o2 dot pl // o like oxygen not 0 like zero
console program in c programing language
===============================================================
==============================================
Structure of a program or how to analyze the program
Creating graphic:
* memory array
* save it to the disk as a pgm file
* convert pgm file to png usnigng Image Magic convert
* map it to the c plane: for each pixel of plane compute c or lambda using map_parameter
==========================================
---------------------------------
indent d.c
default is gnu style
-------------------
c console progam
export OMP_DISPLAY_ENV="TRUE"
gcc d.c -lm -Wall -march=native -fopenmp
time ./a.out > b.txt
gcc e.c -lm -Wall -march=native -fopenmp
time ./a.out
time ./a.out >a.txt
./g.sh
============================
gcc e.c -lm -Wall -march=native -fopenmp -pg
gprof ./a.out > p.txt
*/
#include <stdio.h>
#include <stdlib.h> // malloc
#include <string.h> // strcat
#include <math.h> // M_PI; needs -lm also
#include <complex.h> // complex numbers : https://stackoverflow.com/questions/6418807/how-to-work-with-complex-numbers-in-c
#include <omp.h> // OpenMP
#define kMax 12
// https://sourceforge.net/p/predef/wiki/Standards/
#if defined(__STDC__)
#define PREDEF_STANDARD_C_1989
#if defined(__STDC_VERSION__)
#if (__STDC_VERSION__ >= 199409L)
#define PREDEF_STANDARD_C_1994
#endif
#if (__STDC_VERSION__ >= 199901L)
#define PREDEF_STANDARD_C_1999
#endif
#endif
#endif
/* --------------------------------- global variables and consts ------------------------------------------------------------ */
// each typedef should have different range !!!
/* Representation FunctionType
https://mrob.com/pub/muency/representationfunction.html
function defining relation between data and the image
*/
typedef enum {
LSM =100,
LCM = 101,
DEM = 102,
Unknown = 103,
BD = 104,
MBD = 105,
SAC,
DLD,
ND,
NP,
POT,
Blend
} RepresentationFunctionTypeT;
// virtual 2D array and integer ( screen) coordinate
// Indexes of array starts from 0 not 1
//unsigned int ix, iy; // var
static unsigned int ixMin = 0; // Indexes of array starts from 0 not 1
static unsigned int ixMax; //
static unsigned int iWidth; // horizontal dimension of array
static unsigned int iyMin = 0; // Indexes of array starts from 0 not 1
static unsigned int iyMax; //
static unsigned int iHeight = 1000; //
// The size of array has to be a positive constant integer
static unsigned int iSize; // = iWidth*iHeight;
// ----------memmory 1D arrays ==================
// unsigned char = for 1 byte ( 8 bit) colors
unsigned char *data;
unsigned char *edge;
// unsigned int i; // var = index of 1D array
//static unsigned int iMin = 0; // Indexes of array starts from 0 not 1
static unsigned int iMax; // = i2Dsize-1 =
// The size of array has to be a positive constant integer
// unsigned int i1Dsize ; // = i2Dsize = (iMax -iMin + 1) = ; 1D array with the same size as 2D array
// on the initial plane , before transformation
int iInvDisplayARatio = 10;
double DisplayAspectRatio ; // https://en.wikipedia.org/wiki/Aspect_ratio_(image)
/*
primary separators
c = m[i]
between bands ( parts of chaotic part = main antenna)
https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/misiurewicz#primary_separator
https://digital.csic.es/bitstream/10261/8916/3/Pastor02%20pre.pdf G. Pastor, M. Romera, G. Álvarez and F. Montoya, "Operating with external arguments in the Mandelbrot set antenna", Physica D, 171 (2002), 52-71
https://www.tic.itefi.csic.es/gerardo/publica/Romera97a.pdf A scaling constant equal to unity in 1D- quadratic maps by M. ROMERA, G. PASTOR and F. MONTOYA
*/
double m[kMax] = {
-2.000000000000000,
-1.543689012692076, // c = -1.543689012692076 +0.000000000000000 i period = 10000
-1.430357632451307, // c = -1.430357632451307 +0.000000000000000 i period = 10000
-1.407405118164702, //c = -1.407405118164702 +0.000000000000000 i period = 10000
-1.402492176358564,
-1.401441494253588,
-1.401216504309415,
-1.401168320839301,
-1.401158001505211,
-1.401155791424613,
-1.401155318093230,
-1.401155216720152
};
const complex double cf = -1.401155189093314712; //the Feigenbaum point -1.401155 = m[infinity]
//c lambda
const complex double critical_point = 0.0; // 0.5};
// parameter plane
double xMin ; //-0.05;
double xMax ; //0.75;
double yMin ; //-0.1;
double yMax ; //0.7;
double PixelWidth; // =(CxMax-CxMin)/ixMax;
double PixelHeight; // =(CyMax-CyMin)/iyMax;
double plane_radius;
complex double plane_center;
double zoom;
const int iterMax_LSM = 100100;
const int iterMax_DEM = 100100;
// EscapeRadius for bailout test
double ER = 100.0;
double ER2;
double ER_DEM = 100.0;
double ER2_DEM;
/* colors = shades of gray from 0 to 255 */
unsigned char iColorOfExterior = 250;
unsigned char iColorOfInterior = 200;
unsigned char iColorOfBoundary = 0;
unsigned char iColorOfUnknown = 30;
/* ------------------------------------------ functions -------------------------------------------------------------*/
inline double clamp(double x, double lo, double hi) {
return fmin(fmax(x, lo), hi);
}
//------------------complex numbers -----------------------------------------------------
inline double cabs2(complex double z) {
return creal(z) * creal(z) + cimag(z) * cimag(z);
}
// from screen to world coordinate ; linear mapping
// uses global cons
static inline double Give_x (const int ix)
{
return (xMin + ix * PixelWidth);
}
// uses global cons
static inline double Give_y (const int iy) {
return (yMax - iy * PixelHeight); // reverse y axis
}
static inline complex double Give_c (const int ix, const int iy)
{
double x = Give_x (ix);
double y = Give_y (iy);
return x + y * I;
}
complex double fc( const double complex z , const complex double c ){
return z*z +c;
}
/* ----------- array functions = drawing -------------- */
/* gives position of 2D point (ix,iy) in 1D array ; uses also global variable iWidth */
static inline unsigned int Give_i (const int ix, const int iy)
{
return ix + iy * iWidth;
}
// ***********************************************************************************************
// ********************** edge detection usung Sobel filter ***************************************
// ***************************************************************************************************
// from Source to Destination
int ComputeBoundaries(const unsigned char S[], unsigned char D[])
{
unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
unsigned int i; /* index of 1D array */
/* sobel filter */
unsigned char G, Gh, Gv;
// boundaries are in D array ( global var )
// clear D array
memset(D, iColorOfExterior, iSize*sizeof(*D)); //
// printf(" find boundaries in S array using Sobel filter\n");
#pragma omp parallel for schedule(dynamic) private(i,iY,iX,Gv,Gh,G) shared(iyMax,ixMax)
for(iY=1;iY<iyMax-1;++iY){
for(iX=1;iX<ixMax-1;++iX){
Gv= S[Give_i(iX-1,iY+1)] + 2*S[Give_i(iX,iY+1)] + S[Give_i(iX-1,iY+1)] - S[Give_i(iX-1,iY-1)] - 2*S[Give_i(iX-1,iY)] - S[Give_i(iX+1,iY-1)];
Gh= S[Give_i(iX+1,iY+1)] + 2*S[Give_i(iX+1,iY)] + S[Give_i(iX-1,iY-1)] - S[Give_i(iX+1,iY-1)] - 2*S[Give_i(iX-1,iY)] - S[Give_i(iX-1,iY-1)];
G = sqrt(Gh*Gh + Gv*Gv);
i= Give_i(iX,iY); /* compute index of 1D array from indices of 2D array */
if (G==0) {D[i]=255;} /* background */
else {D[i]=0;} /* boundary */
}
}
return 0;
}
// copy from Source to Destination
int CopyBoundaries(const unsigned char S[], unsigned char D[])
{
unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
unsigned int i; /* index of 1D array */
fprintf(stderr, "copy boundaries from S array to D array \n");
for(iY=1;iY<iyMax-1;++iY)
for(iX=1;iX<ixMax-1;++iX)
{i= Give_i(iX,iY); if (S[i]==0) D[i]=0;}
return 0;
}
// ***************************************************************************************************************************
// ************************** LSM*****************************************
// ****************************************************************************************************************************
unsigned char ComputeColorOfLSM( complex double p){
int nMax = iterMax_LSM;
unsigned char iColor;
int n;
complex double z = critical_point;
for (n=0; n < nMax; n++){ //forward iteration
if (cabs2(z) > ER2) break; // esacping
z = fc(z,p); // for speed only one family here without switch
//z = f(FamilyType, z,p); /* forward iteration : complex quadratic polynomial */
}
if (n ==nMax)
{iColor = 0;} // interior = non escaping set
else iColor = 255 - 255.0 * ((double) n)/60; // nMax or lower walues in denominator ; exterior = escaping set
return iColor;
}
// ***************************************************************************************************************************
// ************************** DEM = exterior DE Method where DE = Distance Estimation only for z^+c family !!!! ************
// ****************************************************************************************************************************
/*
*c = cexp(c0) + t->center;
*dc = dc0 * cexp(c0);
}
*/
unsigned char ComputeDolorOfDE(const double complex C )
{
int i=0; // iteration
double complex Z= 0.0; // initial value for iteration Z0
double R; // =radius = cabs(Z)
//double D;
double complex dC = 1.0; // derivative
double de; // = 2 * z * log(cabs(z)) / dc;
int iMax = iterMax_DEM;
unsigned char iColor;
// iteration = computing the orbit
for(i=0;i<iMax;i++)
{
// only for c family
dC = 2 * Z * dC + 1.0;
Z = fc(Z, C); // Z*Z+C; // https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/qpolynomials
if(cabs2(Z) > ER2_DEM) break; // exterior of M set
} // for(i=0
if (i == iMax)
{iColor = iColorOfInterior;}// interior
else { // exterior and boundary
R = cabs(Z);
//cd2 = cd2;
de = 2.0 * R * log(R) / cabs(dC) ; // 2 * cabs(z) * log(cabs(z)) / cabs(dc);
// choose only ascending part of y = tanh(x) graph y in [ 0.0,1.0] range
//d = clamp( d, 0.0, 1.0);
// gray gradient
double d = tanh(de/PixelWidth ); // map to [-3,3] range
d = clamp( d, 0.0, 1.0);
// map from floating point in [0,1] range to integer in [0.255] range
iColor = ((int)(d *255.0)) ;
}
return iColor;
}
/* ==================================================================================================
============================= Draw functions ===============================================================
=====================================================================================================
*/
unsigned char ComputeColor(const RepresentationFunctionTypeT RepresentationFunctionType, const complex double c ){
unsigned char iColor= 0;
switch(RepresentationFunctionType){
case LSM :{iColor = ComputeColorOfLSM(c); break;}
case DEM : {iColor = ComputeDolorOfDE( c); break; } //
default: {}
}
return iColor;
}
unsigned char GiveColor(const RepresentationFunctionTypeT RepresentationFunctionType, const int ix, const int iy){
complex double c = Give_c(ix,iy);
unsigned char iColor = ComputeColor(RepresentationFunctionType, c);
return iColor;
}
// plots raster point (ix,iy) = computes it's color and save it to the array A
int DrawPoint (const RepresentationFunctionTypeT RepresentationFunctionType, const int ix, const int iy, unsigned char A[])
{
unsigned char iColor = GiveColor( RepresentationFunctionType, ix, iy);
unsigned int i = Give_i (ix, iy); /* compute index of 1D array from indices of 2D array */
A[i] = iColor ; //
return 0;
}
// fill array
// uses global var : ...
// scanning complex plane
int DrawImage (const int k, const RepresentationFunctionTypeT RepresentationFunctionType, unsigned char A[])
{
unsigned int ix, iy; // pixel coordinate
fprintf(stderr, "compute image %d RepresentationFunctionType = %d \t \n", k, RepresentationFunctionType);
// for all pixels of image
#pragma omp parallel for schedule(dynamic,1) private(ix,iy) shared(A, ixMax , iyMax)
// #pragma omp parallel for schedule(dynamic, 1)
for (iy = iyMin; iy <= iyMax; ++iy){
fprintf (stderr, " %d from %d \r", iy, iyMax); //info
for (ix = ixMin; ix <= ixMax; ++ix)
{DrawPoint(RepresentationFunctionType, ix, iy, A);} //
}
return 0;
}
// *******************************************************************************************
// ********************************** save A array to pgm file ****************************
// *********************************************************************************************
int SaveImage(const unsigned char A[], const char *shortName )
{
FILE *fp;
const unsigned int MaxColorComponentValue = 255; /* color component is coded from 0 to 255 ; it is 8 bit color file */
// https://programmerfish.com/create-output-file-names-using-a-variable-in-c-c/
char fileName[512];
const char* fileType = ".pgm";
sprintf(fileName,"%s%s", shortName, fileType); //
char long_comment[200];
sprintf (long_comment, "one parameter family of complex quadratic polynomial, parameter plane ");
// save image array 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", long_comment, iWidth, iHeight, MaxColorComponentValue); // write header to the file
size_t rSize = fwrite (A, sizeof(A[0]), iSize, fp); // write whole array with image data bytes to the file in one step
fclose (fp);
// info
if ( rSize == iSize)
{
printf ("File %s saved ", fileName);
if (long_comment == NULL || strlen (long_comment) == 0)
printf ("\n");
else { printf (". Comment = %s \n", long_comment); }
}
else {printf("wrote %zu elements out of %u requested\n", rSize, iSize);}
return 0;
}
/*
********************************************* info
*/
int PrintInfoAboutProgam()
{
//
printf (" \n");
printf("gcc version: %d.%d.%d\n",__GNUC__,__GNUC_MINOR__,__GNUC_PATCHLEVEL__); // https://stackoverflow.com/questions/20389193/how-do-i-check-my-gcc-c-compiler-version-for-my-eclipse
// OpenMP version is displayed in the console
return 0;
}
// uses global var, plane before transformation,
// local set up
int set_plane(const int k){
xMin = m[k];
if (k+1 == kMax)
{fprintf(stderr, " bad range in set_plane function\n"); return 1;}
// else
xMax = m[k+1]; //0.75;
//
plane_radius = (xMax - xMin)*DisplayAspectRatio/2.0 ;
yMin = -plane_radius; // inv
yMax = plane_radius; //0.7;
/* Pixel sizes of the initial plane, before transformation !!!! can be set globally */
PixelWidth = (xMax - xMin) / ixMax; // ixMax = (iWidth-1) step between pixels in world coordinate
PixelHeight = (yMax - yMin) / iyMax;
//ratio = ((xMax - xMin) / (yMax - yMin)) / ((double) iWidth / (double) iHeight); // it should be 1.000 ...
zoom = 1.0/plane_radius;
//
return 0;
}
// *****************************************************************************
//;;;;;;;;;;;;;;;;;;;;;; program setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
// **************************************************************************************
// globa; setup = the same for all pixels
int setup ( )
{
fprintf (stderr, "setup start\n");
DisplayAspectRatio = 1.0 / iInvDisplayARatio;
/* 2D array ranges */
iWidth = iHeight * iInvDisplayARatio;
iSize = iWidth * iHeight; // size = number of points in array
iyMax = iHeight - 1; // Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].
ixMax = iWidth - 1;
/* 1D array ranges */
// i1Dsize = i2Dsize; // 1D array with the same size as 2D array
iMax = iSize - 1; // Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].
ER2_DEM = ER_DEM*ER_DEM;
ER2 = ER*ER;
/* create dynamic 1D arrays for colors ( shades of gray ) */
data = malloc (iSize * sizeof (unsigned char));
edge = malloc (iSize * sizeof (unsigned char));
//
if (data == NULL || edge == NULL ){
fprintf (stderr, " Setup error : Could not allocate memory");
return 1;
}
fprintf (stderr," end of setup \n");
return 0;
} // ;;;;;;;;;;;;;;;;;;;;;;;;; end of the setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
const char* GiveName(const int k, const RepresentationFunctionTypeT RepresentationFunctionType)
{
static char Name[512];
sprintf(Name,"%d_%d", k, RepresentationFunctionType);
return Name;
}
int PrintInfoAboutImage(){
fprintf(stdout, "zoom = %.16e\n",zoom);
fprintf(stdout, "plane radius = %.16e\n",plane_radius);
fprintf(stdout, "PixelWidth = %.16e \n", PixelWidth);
fprintf(stdout, "xMin = %.16e \t xMax = %.16e\n",xMin, xMax); //
fprintf(stdout, "yMin = %.16e \t yMax = %.16e\n",yMin, yMax);
printf("==========================================================================================================================\n\n\n\n");
return 0;
};
int MakeImages( const int k){
set_plane(k);
const char *Name;
DrawImage(k, LSM, data);
Name = GiveName(k, LSM);
SaveImage(data, Name);
ComputeBoundaries(data,edge);
Name = GiveName(k, LCM);
SaveImage(edge, Name);
//CopyBoundaries(edge, data);
//shortName = GiveName("LSCM", ProjectionType);
//SaveImage(data, shortName);
DrawImage(k, DEM, data);
Name = GiveName(k, DEM);
SaveImage(data, Name);
PrintInfoAboutImage();
return 0;
}
int end(){
fprintf (stderr," allways free memory (deallocate ) to avoid memory leaks \n"); // https://en.wikipedia.org/wiki/C_dynamic_memory_allocation
free (data);
free(edge);
PrintInfoAboutProgam();
return 0;
}
// ********************************************************************************************************************
/* ----------------------------------------- main -------------------------------------------------------------*/
// ********************************************************************************************************************
int main () {
setup();
for (int k=0; k<kMax-1; ++k) {
MakeImages( k);
}
end();
return 0;
}
bash source code
#!/bin/bash
# script file for BASH
# which bash
# save this file as d.sh
# chmod +x d.sh
# ./d.sh
# checked in https://www.shellcheck.net/
printf "make pgm files \n"
gcc e.c -lm -Wall -march=native -fopenmp -O3
if [ $? -ne 0 ]
then
echo ERROR: compilation failed !!!!!!
exit 1
fi
export OMP_DISPLAY_ENV="TRUE"
printf "display OMP info \n"
printf "run the compiled program\n"
time ./a.out > e.txt
export OMP_DISPLAY_ENV="FALSE"
printf "change Image Magic settings\n"
export MAGICK_WIDTH_LIMIT=100MP
export MAGICK_HEIGHT_LIMIT=100MP
printf "convert all pgm files to png using Image Magic v 6 convert \n"
# for all pgm files in this directory
for file in *.pgm ; do
# b is name of file without extension
b=$(basename "$file" .pgm)
# convert using ImageMagic
convert "${b}".pgm -resize 5000x500 "${b}".png
echo "$file"
done
printf "delete all pgm files \n"
rm ./*.pgm
echo OK
printf "info about software \n"
bash --version
make -v
gcc --version
convert -version
convert -list resource
# end
make
all:
chmod +x e.sh
./d.sh
Tu run the program simply
make
text output
File 0_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 0_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 0_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 4.3829757679062332e+01 plane radius = 2.2815549365396204e-02 PixelWidth = 4.5635662297022108e-05 xMin = -2.0000000000000000e+00 xMax = -1.5436890126920759e+00 yMin = -2.2815549365396204e-02 yMax = 2.2815549365396204e-02 ========================================================================================================================== File 1_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 1_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 1_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 1.7647362943529524e+02 plane radius = 5.6665690120384473e-03 PixelWidth = 1.1334271451222017e-05 xMin = -1.5436890126920759e+00 xMax = -1.4303576324513070e+00 yMin = -5.6665690120384473e-03 yMax = 5.6665690120384473e-03 ========================================================================================================================== File 2_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 2_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 2_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 8.7136423270508431e+02 plane radius = 1.1476257143302471e-03 PixelWidth = 2.2954809767581698e-06 xMin = -1.4303576324513070e+00 xMax = -1.4074051181647020e+00 yMin = -1.1476257143302471e-03 yMax = 1.1476257143302471e-03 ========================================================================================================================== File 3_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 3_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 3_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 4.0708807043089660e+03 plane radius = 2.4564709030689970e-04 PixelWidth = 4.9134331494529391e-07 xMin = -1.4074051181647020e+00 xMax = -1.4024921763585640e+00 yMin = -2.4564709030689970e-04 yMax = 2.4564709030689970e-04 ========================================================================================================================== File 4_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 4_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 4_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 1.9035253294292892e+04 plane radius = 5.2534105248802643e-05 PixelWidth = 1.0507871836944223e-07 xMin = -1.4024921763585640e+00 xMax = -1.4014414942535880e+00 yMin = -5.2534105248802643e-05 yMax = 5.2534105248802643e-05 ========================================================================================================================== File 5_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 5_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 5_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 8.8892861738808468e+04 plane radius = 1.1249497208654091e-05 PixelWidth = 2.2501244541762358e-08 xMin = -1.4014414942535880e+00 xMax = -1.4012165043094149e+00 yMin = -1.1249497208654091e-05 yMax = 1.1249497208654091e-05 ========================================================================================================================== File 6_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 6_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 6_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 4.1508010844294040e+05 plane radius = 2.4091735056908092e-06 PixelWidth = 4.8188288942710456e-09 xMin = -1.4012165043094149e+00 xMax = -1.4011683208393011e+00 yMin = -2.4091735056908092e-06 yMax = 2.4091735056908092e-06 ========================================================================================================================== File 7_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 7_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 7_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 1.9381095548731417e+06 plane radius = 5.1596670450626549e-07 PixelWidth = 1.0320366126737983e-09 xMin = -1.4011683208393011e+00 xMax = -1.4011580015052110e+00 yMin = -5.1596670450626549e-07 yMax = 5.1596670450626549e-07 ========================================================================================================================== File 8_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 8_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 8_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 9.0494437258658111e+06 plane radius = 1.1050402989321029e-07 PixelWidth = 2.2103016280270084e-10 xMin = -1.4011580015052110e+00 xMax = -1.4011557914246131e+00 yMin = -1.1050402989321029e-07 yMax = 1.1050402989321029e-07 ========================================================================================================================== File 9_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 9_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 9_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 4.2253695212030053e+07 plane radius = 2.3666569159974673e-08 PixelWidth = 4.7337872107160060e-11 xMin = -1.4011557914246131e+00 xMax = -1.4011553180932299e+00 yMin = -2.3666569159974673e-08 yMax = 2.3666569159974673e-08 ========================================================================================================================== File 10_100.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 10_101.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane File 10_102.pgm saved . Comment = one parameter family of complex quadratic polynomial, parameter plane zoom = 1.9729104026429817e+08 plane radius = 5.0686538966004948e-09 PixelWidth = 1.0138321625363526e-11 xMin = -1.4011553180932299e+00 xMax = -1.4011552167201520e+00 yMin = -5.0686538966004948e-09 yMax = 5.0686538966004948e-09 ========================================================================================================================== gcc version: 11.2.0
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