File:Julia set for z^2-0.101096363845622 +0.956286510809142*I.png

#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 j.c -lm -Wall -fopenmp

./a.out >ed.ppm   // P6 = binary Portable PixMap see https://en.wikipedia.org/wiki/Netpbm#File_formats


*/



complex double examples [6] = {-0.101096363845622 +0.956286510809142*I, 0.397391822296541  +0.133511204871878*I, I, -0.0649150006787816892861875745218343125883 +0.76821968591243610206311097043854440463 *I, -0.239026451915233+0.415516996006582*I, 0};

const double pi = 3.141592653589793;
int q = 2 ; // degree of multibrot set

/*
 
complex double f(complex double z, int q){ return cpow(z,q) + c;}
complex double d(complex double z, int q) {return q*cpow(z, q-1); }

*/
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}




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()
{
  const int aa = 4;
  const int w = 800 * aa;
  const int h = 800 * aa;
  const int n = 1024;
  const double r = 2;
  const double px = r / (h/2);
  const double r2 = 25 * 25;
  unsigned char *img = malloc(3 * w * h);
  
  double _Complex c = examples[q-2];

  #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 / aa);
      }
      
      // 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;
}