Question

I am trying to create a mandelbrot image using c++/opengl. Below is the simple code that i have came up with so far and the image that comes out:

 #include<GL/gl.h>
 #include <GL/glu.h>
 #include <GL/glut.h>
 #include <math.h>
 #include <stdio.h>
 #include <stdlib.h>

 double dividecubesby  = 300;
 const double left = -2.0;
 const double right = 2.0;
 const double bottom = -2.0;
 const double top = 2.0;
 int maxiteration = 90;

 int mandtest(double Cr, double Ci){

   double Zr = 0.0;
   double Zi = 0.0;
   int times = 0;

   Zr = Zr+Cr;
   Zi = Zi+Ci;

      while ((((Zr*Zr)+(Zi*Zi))<4) && (times < maxiteration)){


        Zr = (Zr*Zr)-(Zi*Zi);
        Zi = 2*Zr*Zi;
        Zr = Zr+Cr;
        Zi = Zi+Ci;                
        times = times+1;  

      }
 return times;



void display(void)
{
        glClear(GL_COLOR_BUFFER_BIT);
        glColor3f(1.0f,1.0f,1.0f);
        double real = left;//this is the real part of  the order-pair in the cube
        double image = top;// this is the image part of the order-pair in the cube
        double deltax = ((right - left)/(dividecubesby));//this means 4/300
        double deltay = ((top- bottom)/(dividecubesby));// this means 4/300

glBegin(GL_POINTS);

    for(double x= left;x<=right;x += deltax ){


        for(double y= bottom; y<=top;y +=  deltay ){

            if((mandtest(x,y))==maxiteration){

                glColor3f(1.0f,1.0f,1.0f); 
                            glVertex2f(x,y);

            }

            else {
                glColor3f(0.0f,0.0f,(float)mandtest(x,y)/maxiteration);
                                    glVertex2f(x,y);
            }

        }
    }
    glEnd();

glFlush();

}

void init(void)
{
//select clearing (background) color
    glClearColor(0.0, 0.0, 0.0, 0.0);

        //initialize viewing values 
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
//glortho(left,right,bottom,top,near,far)
    gluOrtho2D(-2.0, 2.0, -2.0, 2.0);
}


int main(int argc, char ** argv)
{   
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
glutInitWindowSize(dividecubesby,dividecubesby);
glutCreateWindow("A Simple OpenGL Windows Application with GLUT");
init();
glutDisplayFunc(display);
glutMainLoop();


    return 0;
}

Answer 1

In

    Zr = (Zr*Zr)-(Zi*Zi);
    Zi = 2*Zr*Zi;
    Zr = Zr+Cr;
    Zi = Zi+Ci;

You use the new Zr to calculate Zi, that yields wrong results, make it

    double temp = (Zr*Zr)-(Zi*Zi);
    Zi = 2*Zr*Zi;
    Zr = temp+Cr;
    Zi = Zi+Ci;

to get better results: