I am trying to adapt the code here : http://code.activestate.com/recipes/577166-newton-fractals/ into C and am having some trouble. I am using C99's complex type.
I basically have tried a few different approaches which haven't worked. On every pixel it goes all the way to the maximum iteration every time, so the image comes out as a solid color.
Is there soemthing I have fundementally wrong about the way the types work in C, it seems like it should work, I reconstructed the algorithm pretty exactly.
//newt.c
#include <stdio.h>
#include <stdlib.h>
#include <complex.h>
#include <float.h>
#include <math.h>
complex f(complex z);
const int WIDTH = 512, HEIGHT = 512;
const double SCALED_X_MAX = 1.0;
const double SCALED_X_MIN = -1.0;
const double SCALED_Y_MAX = 1.0;
const double SCALED_Y_MIN = -1.0;
const int MAX_ITERATIONS = 20;
const int EPSILON = 1e-3;
int main(int argc, char **argv) {
const double SCALED_WIDTH = SCALED_X_MAX - SCALED_X_MIN ;
const double SCALED_HEIGHT = SCALED_Y_MAX - SCALED_Y_MIN ;
FILE * image = fopen("newton.ppm", "w") ;
fprintf(image, "P3\n");
fprintf(image, "%d %d\n" , WIDTH , HEIGHT ) ;
fprintf(image, "%d\n", 255) ;
for ( int y = 0 ; y < HEIGHT ; ++y) {
double zy = y * (SCALED_HEIGHT)/(HEIGHT-1) + SCALED_Y_MIN;
for ( int x = 0 ; x < WIDTH ; ++x ) {
double zx = x * (SCALED_WIDTH)/(WIDTH-1) + SCALED_X_MIN;
complex z = zx + zy*I;
int iteration = 0;
while(iteration < MAX_ITERATIONS ) {
// complex h=sqrt(DBL_EPSILON) + sqrt(DBL_EPSILON)*I;
double h=1e-6;
/*
complex zph = z + h;
complex dz = zph - z;
complex slope = (f(zph) - f(z))/dz;
*/
complex volatile dz = (f(z + (h+h*I)) - f(z)) / (h+I*h) ;
complex z0 = z - f(z) / dz;
//fprintf(stdout,"%f \n", cabs(z0 - z ));
if ( cabs(z0 - z) < EPSILON){
break;
}
z = z0;
iteration++;
}
if (iteration != MAX_ITERATIONS) fprintf(stdout, "%d " , iteration );
fprintf(image,"%3d %3d %3d ", iteration % 4 * 64 ,
iteration % 8 * 32 ,
iteration % 16 * 16);
}
fprintf(image, "\n") ;
}
fclose(image) ;
exit(0);
}
complex f(complex z ) {
return cpow(z,3)-1.0 ;
}
After checking over the complex maths and not seeing any problems I noticed that your error is simply due to the integer division in the line
zy = y * (SCALED_HEIGHT)/(HEIGHT-1) + SCALED_Y_MIN;
and similarly for zx. Because (SCALED_HEIGHT) and (HEIGHT-1) are both integers this is not going to give you the floating point result you require. Try using:
zy = y * SCALED_HEIGHT * 1.0/(HEIGHT-1) + SCALED_Y_MIN;
and similarly for zx.
EDIT: Sorry the above was in error. Your SCALED_HEIGHT was in fact double so the above was actually ok. The real problem is simply in the line
const int EPSILON = 1e-3;
This will in fact always return zero, because it's an integer. You need to make EPSILON a floating point type.