#include <complex.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <omp.h> //OpenM
/*
fork of
mandelbrot-book how to write a book about the Mandelbrot set by Claude Heiland-Alle
https://code.mathr.co.uk/mandelbrot-book/blob/HEAD:/book/
https://stackoverflow.com/questions/77135883/why-do-my-functions-not-work-in-parallel
gcc c.c -lm -Wall -fopenmp
./a.out >ed.ppm // P6 = binary Portable PixMap see https://en.wikipedia.org/wiki/Netpbm#File_formats
convert ed.ppm -resize 25% ed.png
*/
const double pi = 3.141592653589793;
int q = 2 ; // degree of multibrot set
complex double f(complex double z, complex double c){ return z*z + c;} // multibrot z^q + c
complex double d(complex double z) {return 2*z; } // q*z^{q-1} derivative
double cnorm(double _Complex z) // https://stackoverflow.com/questions/6363247/what-is-a-complex-data-type-and-an-imaginary-data-type-in-c
{
return creal(z) * creal(z) + cimag(z) * cimag(z);
}
void hsv2rgb(double h, double s, double v, int *red, int *grn, int *blu) {
double i, f, p, q, t, r, g, b;
int ii;
if (s == 0.0) { r = g = b = v; } else {
h = 6 * (h - floor(h));
ii = i = floor(h);
f = h - i;
p = v * (1 - s);
q = v * (1 - (s * f));
t = v * (1 - (s * (1 - f)));
switch(ii) {
case 0: r = v; g = t; b = p; break;
case 1: r = q; g = v; b = p; break;
case 2: r = p; g = v; b = t; break;
case 3: r = p; g = q; b = v; break;
case 4: r = t; g = p; b = v; break;
default:r = v; g = p; b = q; break;
}
}
*red = fmin(fmax(255 * r + 0.5, 0), 255);
*grn = fmin(fmax(255 * g + 0.5, 0), 255);
*blu = fmin(fmax(255 * b + 0.5, 0), 255);
}
int main()
{
// integer size of the image
const int w = 8000 ;
const int h = 8000 ;
const int n = 1024;
const double r = 2.0; // plane radius
const double px = r / (h/2);
const double r2 = 25 * 25; // escape radius (ER) = r so r2 = ER*ER
unsigned char *img = malloc(3 * w * h);
double _Complex c = -1.4011551890;
#pragma omp parallel for schedule(dynamic)
for (int j = 0; j < h; ++j)
{
double y = (h/2 - (j + 0.5)) / (h/2) * r;
for (int i = 0; i < w; ++i)
{
double x = (i + 0.5 - w/2) / (h/2) * r; // for q=2 add -0.5
double _Complex z = x + I * y;
double _Complex dz = 1.0; // first derivative of zn with respect to z
int k;
for (k = 0; k < n; ++k)
{
//
dz = d(z)*dz ;
z = f(z,c);
if (cnorm(z) > r2)
break;
}
// color
double hue = 0, sat = 0, val = 1; // interior color = white
if (k < n)
{ // exterior and boundary color
double _Complex de = 2 * z * log(cabs(z)) / dz;
hue = fmod(1 + carg(de) / (2 * pi), 1); // ? slope of de
sat = 0.25;
val = tanh(cabs(de) / px );
}
// hsv to rgb conversion
int red, grn, blu;
hsv2rgb(hue, sat, val, &red, &grn, &blu);
// save rgb color to array
img[3*(j * w + i)+0] = red;
img[3*(j * w + i)+1] = grn;
img[3*(j * w + i)+2] = blu;
}
}
//
printf("P6\n%d %d\n255\n", w, h);
fwrite(img, 3 * w * h, 1, stdout);
free(img);
return 0;
}
gcc c.c -lm -Wall -fopenmp
./a.out >ed.ppm
convert ed.ppm -resize 25% ed.png
rm ed.ppm
all:
chmod +x c.sh
./c.sh
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