c programming - Mandelbrot set

Question

I am trying to display Mandelbrot set fractal using c programming, openGL, glut on linux. Here is my code. it only displays a dot in the center. not able to figure out where I am going wrong. any help?

#include <GL/glut.h>    // Header File For The GLUT Library
#include <math.h>
#include <complex.h>

int main (int argc, char *argv[])
{
    int i, j, count;
    float re_max=1.0, re_min=-2.0, im_max=1.0, im_min=-1.0 ; //aspect ratio 3/2
    float real_delta = (re_max - re_min)/750;
    float imag_delta = (im_max - im_min)/500;

    double complex x = 0.0 + 0.0 * I;
    double complex z = re_min + im_min * I;

    double absolute_x;

    glutInit(&argc, argv);
    glutInitDisplayMode (GLUT_RGBA | GLUT_DEPTH);
    glutInitWindowPosition(150,150);
    glutInitWindowSize(750,500); // aspect ratio of 3/2
    glutCreateWindow (argv[0]);

    glClearColor (0.1, 0.2, 0.3, 0.0);  // choosing the background color
    glClear (GL_COLOR_BUFFER_BIT);      // setting the color buffer to background color
    glColor4f(0.5,0.7,0.3,0.0);
    glPointSize(1);

    for (i=0, z = re_min + im_min * I ; i<750; i++, z = (re_min + real_delta) + im_min * I)
        {

        for (j=0, z = creal(z) + im_min * I; j<500; j++, z = creal(z) + (im_min + imag_delta) * I)
            {
            count = 0;
            x = 0 + 0*I;

            while ((absolute_x = fabs(x))<=2.0 && count < 64)
            {
                x = (x * x) + z;
                count++;
            }

                if (absolute_x <= 2.0){
                    glBegin(GL_POINTS);
                        glVertex2i(i,j);
                    glEnd();
                }
            }
        }

    glFlush();

    glutMainLoop();

    return (0);

}

Since the coding issue is solved, I am editing this question with the 'correct working code' along with a beautiful picture of the resulting fractal :-)

here is the working code:

#include <GL/glut.h>    // Header File For The GLUT Library
#include <math.h>
#include <complex.h>

int main (int argc, char *argv[])
{
    int i, j, count;
    float re_max=1., re_min=-2.0, im_max=1.0, im_min=-1.0 ; //aspect ratio 3/2
    float real_delta = (re_max - re_min)/750;
    float imag_delta = (im_max - im_min)/500;

    double complex x = 0.0 + 0.0 * I;
    double complex z = re_min + im_min * I;

    double absolute_x;

    glutInit(&argc, argv);
    glutInitDisplayMode (GLUT_RGBA | GLUT_DEPTH);
    glutInitWindowPosition(150,150);
    glutInitWindowSize(750,500); // aspect ratio of 3/2
    glutCreateWindow (argv[0]);

    glClearColor (0.5, 0.2, 0.3, 0.0);  // choosing the background color
    glClear (GL_COLOR_BUFFER_BIT);      // setting the color buffer to background color
    glColor4f(0.5,0.7,0.3,0.0);
    glPointSize(1);

    for (i=0, z = re_min + im_min * I ; i<750; i++, z = (creal(z) + real_delta) + im_min * I)
        {

        for (j=0, z = creal(z) + im_min * I; j<500; j++, z = creal(z) + (cimag(z) + imag_delta) * I)
            {
            count = 0;
            x = 0 + 0*I;

            while ((absolute_x = fabs(x))<=2.0 && count < 64)
            {
                x = (x * x) + z;
                count++;
            }

                if (absolute_x <= 2.0){
                    glBegin(GL_POINTS);
                        glVertex2f(i / 750., j / 500.);;
                    glEnd();
                }
            }
        }

    glFlush();

    glutMainLoop();

    return (0);
}

Answer 1

There're two major mistakes:

1. Your loops looks weird. The loop of i don't change z's value in each of it's iteration, and so is j.
   Suggestion: don't update z in the loop statement which would only make things complicated, instead calculate it directly in the loop body like this:

   for (i=0; i<750; i++)
   {
       for (j=0; j<500; j++)
       {
           z = re_min + real_delta * i + (im_min + imag_delta * j) * I;
           /* other of your codes */
        }
    }
   

2. You're not using OpenGL the right way. By invoking glVertex2i(i, j); you're specifying the coordinates x=i and y=j, but the default viewport of OpenGL is (-1,1)x(-1,1).
   Here're two solutions you could use:

   • Placing a glScalef after created the window to specify the scales on coordinates and don't change other part of your code:

     /* ... */
     glutCreateWindow(argv[0]);
     glScalef(1. / 750., 1. / 500., 1.);
     /* ... */
     

   • Passing scaled coordinates:

     /* don't use this line of your code: */
     /* glVertex2i(i, j); */
     /* while use this line: */
     glVertex2f(i / 750., j / 500.);