Title: DEM/M in c and shadertoy
Post by: Adam Majewski on January 11, 2014, 01:21:15 AM
Hi, There is a nice Mandelbrot set in Shadertoy : Mandelbrot - distance http://www.shadertoy.com/view/lsX3W4 with code by inigo quilez void main(void)
{
vec2 p = -1.0 + 2.0 * gl_FragCoord.xy / iResolution.xy;
p.x *= iResolution.x/iResolution.y;
// animation
float tz = 0.5 - 0.5*cos(0.225*iGlobalTime);
float zoo = pow( 0.5, 13.0*tz );
vec2 cc = vec2(-0.05,.6805) + p*zoo;
// iterate
vec2 z = vec2(0.0);
float m2 = 0.0;
float co = 0.0;
vec2 dz = vec2(0.0);
for( int i=0; i<256; i++ )
{
if( m2>1024.0 ) continue;
// Z' -> 2·Z·Z' + 1
dz = 2.0*vec2(z.x*dz.x-z.y*dz.y, z.x*dz.y + z.y*dz.x ) + vec2(1.0,0.0);
// Z -> Z² + c
z = cc + vec2( z.x*z.x - z.y*z.y, 2.0*z.x*z.y );
m2 = dot(z,z);
co += 1.0;
}
// distance
// d(c) = |Z|·log|Z|/|Z'|
float d = 0.0;
if( co<256.0 ) d = sqrt( dot(z,z)/dot(dz,dz) )*log(dot(z,z));
// do some soft coloring based on distance
d = clamp( 4.0*d/zoo, 0.0, 1.0 );
d = pow( d, 0.25 );
vec3 col = vec3( d );
gl_FragColor = vec4( col, 1.0 );
} I try to do similar ( without animation ) in c ( code below ) but the effect is not good . How can I change it ? TIA c code below : // gcc m.c -lm -Wall -march=native
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
/* iXmax/iYmax = 1 */
unsigned int iSide = 1000; /* side of rectangle in pixels */
unsigned int iXmax; // ((int)(m*iSide)) /* height of image in pixels */
unsigned int iYmax ; //= iSide;
unsigned int iLength; // = (iXmax*iYmax) /* number of pixels */
/* world ( double) coordinate */
double dSide = 1.5;
double CxMin ; // = 0.0;
double CxMax ; // =(m*dSide);
double CyMin ; //= dSide;
double CyMax ; // = dSide;
/* (CxMax-CxMin)/(CyMax-CyMin)==iXmax/iYmax = 1 */
unsigned int IterationMax; // = (iXmax*100) /* proportional to resolution of picture */
double PixelWidth; //= ((CxMax-CxMin)/iXmax)
double PixelHeight ;//= ((CyMax-CyMin)/iYmax)
double CDistanceMax ; //= PixelWidth; /* proportional to pixel size */
/* fc(z) = z*z + c */
double EscapeRadius = 33.0; /* radius of circle around origin; its complement is a target set for escaping points */
double ER2 ; //= (EscapeRadius*EscapeRadius)
/* colors = shades of gray from 0=black to 255=white */
unsigned char iExterior = 245; /* exterior of Julia set */
unsigned char iBoundary = 0; /* border , boundary*/
unsigned char iInterior = 180;
unsigned int f(unsigned int _iX, unsigned int _iY)
/*
gives position of point (iX,iY) in 1D array ; uses also global variables
it does not check if index is good so memory error is possible
*/
{return (_iX + (iYmax-_iY-1)*iXmax );}
/*
estimates distance from point c to nearest point in Julia set
for Fc(z)= z*z + c
z(n+1) = Fc(zn)
this function is based on function mndlbrot::dist from mndlbrot.cpp
from program mandel by Wolf Jung (GNU GPL )
http://www.mndynamics.com/indexp.html
Hyunsuk Kim :
For Julia sets, z is the variable and c is a constant. Therefore df[n+1](z)/dz = 2*f[n]*f'[n] -- you don't add 1.
For the Mandelbrot set on the parameter plane, you start at z=0 and c becomes the variable. df[n+1](c)/dc = 2*f[n]*f'[n] + 1.
http://iquilezles.org/www/articles/distancefractals/distancefractals.htm
*/
// boolean Escape time and DEM/M in one loop
unsigned char GiveColor( double Cx, double Cy, int iMax, double DistanceMax)
{
// C = Cx + Cy* I = point of parameter c-plane
int i; /* iteration number */
double Zx, Zy; /* Z = Zx + Zy*I point of dynamical plane */
double Zx2, Zy2; /* Zx2=Zx*Zx; Zy2=Zy*Zy */
double temp;
double absZ2;
// http://en.wikipedia.org/wiki/Complex_quadratic_polynomial
// first derivative of fc(zcr) with respect to c = dZ = dfc(zcr)/dc = 2*Z*dZ = dZx + dZy*I
double dZx = 0.0;
double dZy = 0.0;
double absdZ2; // = abs(dZ)* abs(dZ) = dZx*dZx + dZy*dZy
double distance;
unsigned char color = iInterior;
/* initial value of orbit = critical point zcr = 0 */
Zx=0.0;
Zy=0.0;
//
Zx2 = Zx*Zx;
Zy2 = Zy*Zy;
absZ2= Zx*Zx + Zy*Zy;
absdZ2= dZx*dZx + dZy*dZy;
// iteration of critical point z= 0 on the dynamical z-plane
for (i=0; i<iMax; i++)
{ // check if not escaping : abs(z)>ER
if (absZ2 > ER2 ) { color= iExterior; break ; } // exterior when escapes
//if (absdZ2 > 1e60) { return iInterior; } // interior when derivative explodes
// z = fc(z) = z*z + c
Zy=2*Zx*Zy + Cy;
Zx=Zx2-Zy2 +Cx;
/* first derivative zp = 2*z*zp = xp + yp*i; */
temp = 2*(Zx*dZx - Zy*dZy) + 1.0 ; /* */
dZy = 2*(Zx*dZy + Zy*dZx);
dZx = temp;
// abs
Zx2 = Zx*Zx;
Zy2 = Zy*Zy;
absZ2= Zx2 + Zy2; // nz = x*x + y*y;
absdZ2= dZx*dZx + dZy*dZy; //
};
if (i<iMax)
{
distance = sqrt(absZ2/absdZ2)*log(absZ2); //
distance = pow( distance, 0.25 );
//if (distance > 0.0 && distance<DistanceMax*)
// { //color = ((int)(255.0*distance)) % 255;
// d = sqrt( dot(z,z)/dot(dz,dz) )*log(dot(z,z));
// do some soft coloring based on distance
//d = pow( 4.0*d/zoom, 0.25 );
//if (distance < (DistanceMax)) color = iBoundary ; // bondary = black
// near boundary = shades of gray
color = 255-255*(int)(distance/DistanceMax);
//}
}
// if (nz < bailout) return 1; //still not escaping after iteration , rare
// if (absdZ2 < absZ2) color= iExterior; //includes escaping through 0 // som eiterior points are coded as exterior = error
return color;
} //0.000007
/* --------------------------------------------------------------------------------------------------------- */
int main(){
unsigned int iX,iY, /* indices of 2D virtual array (image) = integer coordinate */
i; /* index of 1D array */
double Cx, Cy;
//int ExtLastIteration; //
unsigned char color;
printf(" Setup \n");
iXmax= iSide; /* height of image in pixels */
iYmax = iSide;
iLength = iXmax*iYmax; /* number of pixels */
CxMin = -2.25;
CxMax = 0.75 ;
CyMin = -dSide;
CyMax = dSide;
IterationMax = 1000 ;
PixelWidth= (CxMax-CxMin)/iXmax;
PixelHeight = (CyMax-CyMin)/iYmax;
ER2 = EscapeRadius*EscapeRadius;
/* dynamic 1D array for colors ( shades of gray ) */
unsigned char *data;
data = malloc( iLength * sizeof(unsigned char) );
if (data == NULL )
{
fprintf(stderr," Could not allocate memory");
return 1;
}
printf(" compute color \n");
for(iY=0;iY<iYmax;++iY){
Cy=CyMin + iY*PixelHeight; /* */
printf("row %u from %u \n",iY, iYmax);
for(iX=0;iX<iXmax;++iX){
Cx=CxMin + iX*PixelWidth;
color=GiveColor(Cx, Cy, IterationMax, PixelWidth);
i= f(iX,iY); /* compute index of 1D array from indices of 2D array */
data[i]=color; /* change the color */
}
}
printf(" save data array to the pgm file \n");
unsigned int length = 30;
char filename[length] ;
snprintf(filename, length, "%.0fe%u%s", EscapeRadius,IterationMax, ".pgm");
char *comment="# ";/* comment should start with # */
const unsigned int MaxColorComponentValue=255; /* color component is coded from 0 to 255 ; it is 8 bit color file */
/* save image to pgm file */
FILE * fp;
fp = fopen(filename,"wb"); /*create new file,give it a name and open it in binary mode */
fprintf(fp,"P5\n %s\n %u\n %u\n %u\n",comment,iXmax,iYmax,MaxColorComponentValue); /*write header to the file*/
fwrite(data,iLength,1,fp); /*write image data bytes to the file in one step */
printf("File %s saved. \n", filename);
fclose(fp);
/* ---------- text file -------------------------------------*/
char tfilename[length] ;
printf(" save graphic data to the text file \n");
snprintf(tfilename, length, "%.0fe%u%s",EscapeRadius, iXmax, ".txt");
/* save info to the file */
fp = fopen(tfilename,"wb"); /*create new file,give it a name and open it in binary mode */
fprintf(fp,"IterationMax = %d \n", IterationMax);
fprintf(fp,"EscapeRadius = %f ER2 = %f \n", EscapeRadius, ER2);
fprintf(fp,"\n" ); /* */
fprintf(fp,"C plane : \n" ); /* */
fprintf(fp,"dSide = %f \n", dSide);
fprintf(fp,"PixelWidth = %f ; PixelHeight = %f \n", PixelHeight, PixelWidth);
fprintf(fp," CxMin = %f \n", CxMin); /* */
fprintf(fp," CxMax = %f \n", CxMax); /* */
fprintf(fp," CyMin = %f \n", CyMin); /* */
fprintf(fp," CyMax = %f \n", CyMax); /* */
fprintf(fp,"\n" );
//
printf("File %s saved. \n", tfilename);
fclose(fp);
printf(" allways free memory \n ");
free(data);
return 0;
}
Title: Re: DEM/M in c and shadertoy
Post by: xenodreambuie on January 11, 2014, 07:46:23 AM
I try to do similar ( without animation ) in c ( code below ) but the effect is not good .
How can I change it ?
One obvious problem is that in the loop, the derivative should be calculated before the new z.
Title: Re: DEM/M in c and shadertoy
Post by: Adam Majewski on January 11, 2014, 09:02:02 AM
Still not the same Help is wellcome /*
to compile :
gcc m.c -lm -Wall -march=native
to run ( Linux console) :
time ./a.out
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
/* iXmax/iYmax = 1 */
unsigned int iSide = 1000; /* side of rectangle in pixels */
unsigned int iXmax; // ((int)(m*iSide)) /* height of image in pixels */
unsigned int iYmax ; //= iSide;
unsigned int iLength; // = (iXmax*iYmax) /* number of pixels */
/* world ( double) coordinate */
double dSide = 1.5;
double CxMin ; // = 0.0;
double CxMax ; // =(m*dSide);
double CyMin ; //= dSide;
double CyMax ; // = dSide;
/* (CxMax-CxMin)/(CyMax-CyMin)==iXmax/iYmax = 1 */
unsigned int IterationMax; // = (iXmax*100) /* proportional to resolution of picture */
double PixelWidth; //= ((CxMax-CxMin)/iXmax)
double PixelHeight ;//= ((CyMax-CyMin)/iYmax)
double CDistanceMax ; //= PixelWidth; /* proportional to pixel size */
/* fc(z) = z*z + c */
double EscapeRadius = 33.0; /* radius of circle around origin; its complement is a target set for escaping points */
double ER2 ; //= (EscapeRadius*EscapeRadius)
/* colors = shades of gray from 0=black to 255=white */
unsigned char iExterior = 245; /* exterior of Julia set */
unsigned char iBoundary = 0; /* border , boundary*/
unsigned char iInterior = 180;
unsigned int f(unsigned int _iX, unsigned int _iY)
/*
gives position of point (iX,iY) in 1D array ; uses also global variables
it does not check if index is good so memory error is possible
*/
{return (_iX + (iYmax-_iY-1)*iXmax );}
/*
estimates distance from point c to nearest point in Julia set
for Fc(z)= z*z + c
z(n+1) = Fc(zn)
this function is based on function mndlbrot::dist from mndlbrot.cpp
from program mandel by Wolf Jung (GNU GPL )
http://www.mndynamics.com/indexp.html
Hyunsuk Kim :
For Julia sets, z is the variable and c is a constant. Therefore df[n+1](z)/dz = 2*f[n]*f'[n] -- you don't add 1.
For the Mandelbrot set on the parameter plane, you start at z=0 and c becomes the variable. df[n+1](c)/dc = 2*f[n]*f'[n] + 1.
http://iquilezles.org/www/articles/distancefractals/distancefractals.htm
*/
// boolean Escape time and DEM/M in one loop
unsigned char GiveColor( double Cx, double Cy, int iMax, double DistanceMax)
{
// C = Cx + Cy* I = point of parameter c-plane
int i; /* iteration number */
double Zx, Zy; /* Z = Zx + Zy*I point of dynamical plane */
double Zx2, Zy2; /* Zx2=Zx*Zx; Zy2=Zy*Zy */
double temp;
double absZ2;
// http://en.wikipedia.org/wiki/Complex_quadratic_polynomial
// first derivative of fc(zcr) with respect to c = dZ = dfc(zcr)/dc = 2*Z*dZ = dZx + dZy*I
double dZx = 0.0;
double dZy = 0.0;
double absdZ2; // = abs(dZ)* abs(dZ) = dZx*dZx + dZy*dZy
double distance;
unsigned char color = iInterior;
/* initial value of orbit = critical point zcr = 0 */
Zx=0.0;
Zy=0.0;
//
Zx2 = Zx*Zx;
Zy2 = Zy*Zy;
absZ2= Zx*Zx + Zy*Zy;
absdZ2= dZx*dZx + dZy*dZy;
// iteration of critical point z= 0 on the dynamical z-plane
for (i=0; i<iMax; i++)
{ // check if not escaping : abs(z)>ER
if (absZ2 > ER2 ) { color= iExterior; break ; } // exterior when escapes
//if (absdZ2 > 1e60) { return iInterior; } // interior when derivative explodes
// in the loop, the derivative should be calculated before the new z
/* first derivative zp = 2*z*zp = xp + yp*i; */
temp = 2*(Zx*dZx - Zy*dZy) + 1.0 ; /* */
dZy = 2*(Zx*dZy + Zy*dZx);
dZx = temp;
// z = fc(z) = z*z + c
Zy=2*Zx*Zy + Cy;
Zx=Zx2-Zy2 +Cx;
// abs
Zx2 = Zx*Zx;
Zy2 = Zy*Zy;
absZ2= Zx2 + Zy2; // nz = x*x + y*y;
absdZ2= dZx*dZx + dZy*dZy; //
};
if (i<iMax)
{
distance = sqrt(absZ2/absdZ2)*log(absZ2); //
distance = pow( 4.0*distance, 0.25 );
//if (distance > 0.0 && distance<DistanceMax*)
// { //color = ((int)(255.0*distance)) % 255;
// d = sqrt( dot(z,z)/dot(dz,dz) )*log(dot(z,z));
// do some soft coloring based on distance
//d = pow( 4.0*d/zoom, 0.25 );
//if (distance < (DistanceMax)) color = iBoundary ; // bondary = black
// near boundary = shades of gray
color = 255*(int)(distance);
//}
}
// if (nz < bailout) return 1; //still not escaping after iteration , rare
// if (absdZ2 < absZ2) color= iExterior; //includes escaping through 0 // som eiterior points are coded as exterior = error
return color;
} //0.000007
/* --------------------------------------------------------------------------------------------------------- */
int main(){
unsigned int iX,iY, /* indices of 2D virtual array (image) = integer coordinate */
i; /* index of 1D array */
double Cx, Cy;
//int ExtLastIteration; //
unsigned char color;
printf(" Setup \n");
iXmax= iSide; /* height of image in pixels */
iYmax = iSide;
iLength = iXmax*iYmax; /* number of pixels */
CxMin = -2.25;
CxMax = 0.75 ;
CyMin = -dSide;
CyMax = dSide;
IterationMax = 1000 ;
PixelWidth= (CxMax-CxMin)/iXmax;
PixelHeight = (CyMax-CyMin)/iYmax;
ER2 = EscapeRadius*EscapeRadius;
/* dynamic 1D array for colors ( shades of gray ) */
unsigned char *data;
data = malloc( iLength * sizeof(unsigned char) );
if (data == NULL )
{
fprintf(stderr," Could not allocate memory");
return 1;
}
printf(" compute color \n");
for(iY=0;iY<iYmax;++iY){
Cy=CyMin + iY*PixelHeight; /* */
printf("row %u from %u \n",iY, iYmax);
for(iX=0;iX<iXmax;++iX){
Cx=CxMin + iX*PixelWidth;
color=GiveColor(Cx, Cy, IterationMax, PixelWidth);
i= f(iX,iY); /* compute index of 1D array from indices of 2D array */
data[i]=color; /* change the color */
}
}
printf(" save data array to the pgm file \n");
unsigned int length = 30;
char filename[length] ;
snprintf(filename, length, "%.0fe%u%s", EscapeRadius,IterationMax, ".pgm");
char *comment="# ";/* comment should start with # */
const unsigned int MaxColorComponentValue=255; /* color component is coded from 0 to 255 ; it is 8 bit color file */
/* save image to pgm file */
FILE * fp;
fp = fopen(filename,"wb"); /*create new file,give it a name and open it in binary mode */
fprintf(fp,"P5\n %s\n %u\n %u\n %u\n",comment,iXmax,iYmax,MaxColorComponentValue); /*write header to the file*/
fwrite(data,iLength,1,fp); /*write image data bytes to the file in one step */
printf("File %s saved. \n", filename);
fclose(fp);
/* ---------- text file -------------------------------------*/
char tfilename[length] ;
printf(" save graphic data to the text file \n");
snprintf(tfilename, length, "%.0fe%u%s",EscapeRadius, iXmax, ".txt");
/* save info to the file */
fp = fopen(tfilename,"wb"); /*create new file,give it a name and open it in binary mode */
fprintf(fp,"IterationMax = %d \n", IterationMax);
fprintf(fp,"EscapeRadius = %f ER2 = %f \n", EscapeRadius, ER2);
fprintf(fp,"\n" ); /* */
fprintf(fp,"C plane : \n" ); /* */
fprintf(fp,"dSide = %f \n", dSide);
fprintf(fp,"PixelWidth = %f ; PixelHeight = %f \n", PixelHeight, PixelWidth);
fprintf(fp," CxMin = %f \n", CxMin); /* */
fprintf(fp," CxMax = %f \n", CxMax); /* */
fprintf(fp," CyMin = %f \n", CyMin); /* */
fprintf(fp," CyMax = %f \n", CyMax); /* */
fprintf(fp,"\n" );
//
printf("File %s saved. \n", tfilename);
fclose(fp);
printf(" allways free memory \n ");
free(data);
return 0;
}
Title: Re: DEM/M in c and shadertoy
Post by: Adam Majewski on January 11, 2014, 09:36:51 AM
distance = sqrt(absZ2/absdZ2)*log(absZ2); //
distance = pow( 4.0*distance, 0.25 );
if (distance<=1.0) color = (int)(255.0*distance);
Now it works. Thx
[code
/*
c console program, for CPU, one thread. numbers type : double
It can be compiled and run under Linux, windows, Mac
It needs gcc
draw :
* check 2 algorithms :
** binary escape time
** add boundary computed by DEM/M
* save it to the pgm file
-----------------------------------------
1.pgm file code is based on the code of Claudio Rocchini
http://en.wikipedia.org/wiki/Image:Color_complex_plot.jpg
create 8 bit color graphic file , portable gray map file = pgm
see http://en.wikipedia.org/wiki/Portable_pixmap
to see the file use external application ( graphic viewer)
I think that creating graphic can't be simpler
---------------------------
2. first it creates data array which is used to store color values of pixels,
fills tha array with data and after that writes the data from array to pgm file.
It alows free ( non sequential) acces to "pixels"
-------------------------------------------
Adam Majewski fraktal.republika.pl
to compile :
gcc m.c -lm -Wall -march=native
to run ( Linux console) :
time ./a.out
convert h6.650000m6650.pgm -resize 800x120 c.png
convert b6.650000m6650.pgm -resize 1600x240 cbig.png
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
/* iXmax/iYmax = 1 */
unsigned int iSide = 1000; /* side of rectangle in pixels */
unsigned int iXmax; // ((int)(m*iSide)) /* height of image in pixels */
unsigned int iYmax ; //= iSide;
unsigned int iLength; // = (iXmax*iYmax) /* number of pixels */
/* world ( double) coordinate */
double dSide = 1.5;
double CxMin ; // = 0.0;
double CxMax ; // =(m*dSide);
double CyMin ; //= dSide;
double CyMax ; // = dSide;
/* (CxMax-CxMin)/(CyMax-CyMin)==iXmax/iYmax = 1 */
unsigned int IterationMax; // = (iXmax*100) /* proportional to resolution of picture */
double PixelWidth; //= ((CxMax-CxMin)/iXmax)
double PixelHeight ;//= ((CyMax-CyMin)/iYmax)
double CDistanceMax ; //= PixelWidth; /* proportional to pixel size */
/* fc(z) = z*z + c */
double EscapeRadius = 33.0; /* radius of circle around origin; its complement is a target set for escaping points */
double ER2 ; //= (EscapeRadius*EscapeRadius)
/* colors = shades of gray from 0=black to 255=white */
unsigned char iExterior = 245; /* exterior of Julia set */
unsigned char iBoundary = 0; /* border , boundary*/
unsigned char iInterior = 0;
unsigned int f(unsigned int _iX, unsigned int _iY)
/*
gives position of point (iX,iY) in 1D array ; uses also global variables
it does not check if index is good so memory error is possible
*/
{return (_iX + (iYmax-_iY-1)*iXmax );}
/*
estimates distance from point c to nearest point in Julia set
for Fc(z)= z*z + c
z(n+1) = Fc(zn)
this function is based on function mndlbrot::dist from mndlbrot.cpp
from program mandel by Wolf Jung (GNU GPL )
http://www.mndynamics.com/indexp.html
Hyunsuk Kim :
For Julia sets, z is the variable and c is a constant. Therefore df[n+1](z)/dz = 2*f[n]*f'[n] -- you don't add 1.
For the Mandelbrot set on the parameter plane, you start at z=0 and c becomes the variable. df[n+1](c)/dc = 2*f[n]*f'[n] + 1.
http://iquilezles.org/www/articles/distancefractals/distancefractals.htm
*/
// boolean Escape time and DEM/M in one loop
unsigned char GiveColor( double Cx, double Cy, int iMax, double DistanceMax)
{
// C = Cx + Cy* I = point of parameter c-plane
int i; /* iteration number */
double Zx, Zy; /* Z = Zx + Zy*I point of dynamical plane */
double Zx2, Zy2; /* Zx2=Zx*Zx; Zy2=Zy*Zy */
double temp;
double absZ2;
// http://en.wikipedia.org/wiki/Complex_quadratic_polynomial
// first derivative of fc(zcr) with respect to c = dZ = dfc(zcr)/dc = 2*Z*dZ = dZx + dZy*I
double dZx = 0.0;
double dZy = 0.0;
double absdZ2; // = abs(dZ)* abs(dZ) = dZx*dZx + dZy*dZy
double distance;
unsigned char color = iInterior;
/* initial value of orbit = critical point zcr = 0 */
Zx=0.0;
Zy=0.0;
//
Zx2 = Zx*Zx;
Zy2 = Zy*Zy;
absZ2= Zx*Zx + Zy*Zy;
absdZ2= dZx*dZx + dZy*dZy;
// iteration of critical point z= 0 on the dynamical z-plane
for (i=0; i<iMax; i++)
{ // check if not escaping : abs(z)>ER
if (absZ2 > ER2 ) { color= iExterior; break ; } // exterior when escapes
//if (absdZ2 > 1e60) { return iInterior; } // interior when derivative explodes
// in the loop, the derivative should be calculated before the new z
/* first derivative zp = 2*z*zp = xp + yp*i; */
temp = 2*(Zx*dZx - Zy*dZy) + 1.0 ; /* */
dZy = 2*(Zx*dZy + Zy*dZx);
dZx = temp;
// z = fc(z) = z*z + c
Zy=2*Zx*Zy + Cy;
Zx=Zx2-Zy2 +Cx;
// abs
Zx2 = Zx*Zx;
Zy2 = Zy*Zy;
absZ2= Zx2 + Zy2; // nz = x*x + y*y;
absdZ2= dZx*dZx + dZy*dZy; //
};
if (i<iMax)
{
distance = sqrt(absZ2/absdZ2)*log(absZ2); //
distance = pow( 4.0*distance, 0.25 );
//if (distance > 0.0 && distance<DistanceMax*)
// { //color = ((int)(255.0*distance)) % 255;
// d = sqrt( dot(z,z)/dot(dz,dz) )*log(dot(z,z));
// do some soft coloring based on distance
//d = pow( 4.0*d/zoom, 0.25 );
//if (distance < (DistanceMax)) color = iBoundary ; // bondary = black
// near boundary = shades of gray
if (distance<=1.0) color = (int)(255.0*distance);
//}
}
// if (nz < bailout) return 1; //still not escaping after iteration , rare
// if (absdZ2 < absZ2) color= iExterior; //includes escaping through 0 // som eiterior points are coded as exterior = error
return color;
} //0.000007
/* --------------------------------------------------------------------------------------------------------- */
int main(){
unsigned int iX,iY, /* indices of 2D virtual array (image) = integer coordinate */
i; /* index of 1D array */
double Cx, Cy;
//int ExtLastIteration; //
unsigned char color;
printf(" Setup \n");
iXmax= iSide; /* height of image in pixels */
iYmax = iSide;
iLength = iXmax*iYmax; /* number of pixels */
CxMin = -2.25;
CxMax = 0.75 ;
CyMin = -dSide;
CyMax = dSide;
IterationMax = 1000 ;
PixelWidth= (CxMax-CxMin)/iXmax;
PixelHeight = (CyMax-CyMin)/iYmax;
ER2 = EscapeRadius*EscapeRadius;
/* dynamic 1D array for colors ( shades of gray ) */
unsigned char *data;
data = malloc( iLength * sizeof(unsigned char) );
if (data == NULL )
{
fprintf(stderr," Could not allocate memory");
return 1;
}
printf(" compute color \n");
for(iY=0;iY<iYmax;++iY){
Cy=CyMin + iY*PixelHeight; /* */
printf("row %u from %u \n",iY, iYmax);
for(iX=0;iX<iXmax;++iX){
Cx=CxMin + iX*PixelWidth;
color=GiveColor(Cx, Cy, IterationMax, PixelWidth);
i= f(iX,iY); /* compute index of 1D array from indices of 2D array */
data[i]=color; /* change the color */
}
}
printf(" save data array to the pgm file \n");
unsigned int length = 30;
char filename[length] ;
snprintf(filename, length, "%.0fe%u%s", EscapeRadius,IterationMax, ".pgm");
char *comment="# ";/* comment should start with # */
const unsigned int MaxColorComponentValue=255; /* color component is coded from 0 to 255 ; it is 8 bit color file */
FILE * fp;
fp = fopen(filename,"wb"); /*create new file,give it a name and open it in binary mode */
fprintf(fp,"P5\n %s\n %u\n %u\n %u\n",comment,iXmax,iYmax,MaxColorComponentValue); /*write header to the file*/
fwrite(data,iLength,1,fp); /*write image data bytes to the file in one step */
printf("File %s saved. \n", filename);
fclose(fp);
printf(" save graphic data to the text file \n");
char tfilename[length] ;
snprintf(tfilename, length, "%.0fe%u%s",EscapeRadius, iXmax, ".txt");
fp = fopen(tfilename,"wb"); /*create new file,give it a name and open it in binary mode */
fprintf(fp,"IterationMax = %d \n", IterationMax);
fprintf(fp,"EscapeRadius = %f ER2 = %f \n", EscapeRadius, ER2);
fprintf(fp,"\n" ); /* */
fprintf(fp,"C plane : \n" ); /* */
fprintf(fp,"Sides = %f x %f \n",CxMax- CxMin, CyMax - CyMin );
fprintf(fp,"PixelWidth = %f ; PixelHeight = %f \n", PixelHeight, PixelWidth);
fprintf(fp," CxMin = %f \n", CxMin); /* */
fprintf(fp," CxMax = %f \n", CxMax); /* */
fprintf(fp," CyMin = %f \n", CyMin); /* */
fprintf(fp," CyMax = %f \n", CyMax); /* */
fprintf(fp," center C = %f ; %f \n",CxMax -(CxMax-CxMin)/2.0, CyMax - (CyMax-CyMin)/2.0); /* */
fprintf(fp,"\n" );
printf("File %s saved. \n", tfilename);
fclose(fp);
printf(" allways free memory \n ");
free(data);
return 0;
}
]
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