gluperspective image gone on dz - glut

Question

I want to do infinite zoom on this fractal. but after few translation on z axis, the image dis appears.
zoom keys are f5 and f6. press shift for fast zoom. f7 is for detailing.
Plz check what i am doing wrong.
// mandelbrot.cpp : Defines the entry point for the console application.
#include "stdafx.h"
int _tmain(int argc, _TCHAR* argv[])
{
return 0;
}
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <glut.h>
float dx=0,dy=0,dz=1.72;
double deltax = 4/300,g=0.01;//this means 4/300
double deltay = 4/300;// this means 4/300
double dividecubesby = 700;
double left = -2.0;
double right = 2.0;
double bottom = -2.0;
double top = 2.0;
int maxiteration = 90;
float c1=0.5,c2=0.5,c3=0.5;
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))
{
double temp = (Zr*Zr)-(Zi*Zi);
Zi = 2*Zr*Zi;
Zr = temp+Cr;
Zi = Zi+Ci;
times = times+1;
}
return times;
}
void display(void)
{
glLoadIdentity();
glViewport(0,0,700,700);
glOrtho(-2.0, 2.0, -2.0, 2.0,-1,1);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
glClear(GL_COLOR_BUFFER_BIT);
glColor3f(1.0, 1.0, 1.0);
glTranslated(dx,dy,dz);
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 += g )
{
for(double y= bottom; y<=top;y += g )
{
if((mandtest(x,y))==maxiteration)
{
glColor3f(c1,c2,c3);
glVertex2f(x,y);
}
else
{
glColor3f((float)mandtest(x,y)/maxiteration,0,(float)mandtest(x,y)/maxiteration);
glVertex2f(x,y);
}
}
}
glEnd();
glFlush();
}
void init(void)
{
glClearColor(0.0, 0.0, 0.0, 0.0);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(45, 700/700, -100,0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glOrtho(-2.0, 2.0, -2.0, 2.0,-1,1);
}
void processSpecialKeys(int key, int x, int y)
{
int mod = glutGetModifiers();
if(key == GLUT_KEY_F1)
{
if (mod == GLUT_ACTIVE_SHIFT)
maxiteration=maxiteration+20;
maxiteration=maxiteration+5;
dividecubesby+=100;
}
if(key == GLUT_KEY_F2)
{
if (mod == GLUT_ACTIVE_SHIFT)
maxiteration=maxiteration-20;
maxiteration=maxiteration-5;
deltax=deltax*5;
deltay=deltay*5;
dividecubesby-=100;
}
if(key == GLUT_KEY_UP)
{
if (mod == GLUT_ACTIVE_SHIFT)
{
dy+=.5;top-=0.5;bottom-=0.5;
}
dy+=0.01;
top-=0.01;
bottom-=0.01;
}
if(key == GLUT_KEY_DOWN)
{
if (mod == GLUT_ACTIVE_SHIFT)
{
dy-=.5;top+=0.5;bottom+=.5;
}
dy-=0.01;
top+=0.01;
bottom+=.01;
}
if(key == GLUT_KEY_LEFT)
{
if (mod == GLUT_ACTIVE_SHIFT)
{
dx-=.5;right+=0.5;left+=0.5;
}
dx-=0.01;
right+=0.01;
left+=0.01;
}
if(key == GLUT_KEY_RIGHT)
{
if (mod == GLUT_ACTIVE_SHIFT)
{
dx+=.5;right-=0.5;left-=0.5;
}
dx+=0.01;
right-=0.01;
left-=0.01;
}
if(key == GLUT_KEY_F5)
{
if (mod == GLUT_ACTIVE_SHIFT)
{
dz+=1;left-=1.2;
right+=1.2;
top+=1.2;
bottom-=1.2;
}
dz+=.01;
left-=0.01099;
right+=0.01099;
top+=0.01099;
bottom-=.01099;
}
if(key == GLUT_KEY_F6) {
if (mod == GLUT_ACTIVE_SHIFT)
{
dz-=1;left+=1.2;
right-=1.2;
top-=1.2;
bottom+=1.2;
}
dz-=.01;
left+=0.01099;
right-=0.01099;
top-=0.01099;
bottom+=.01099;
}
if(key == GLUT_KEY_F4)
{
if (mod == GLUT_ACTIVE_ALT)
exit(0);
}
if(key == GLUT_KEY_F9)
{
c1+=0.01;
}
if(key == GLUT_KEY_F10)
{
c1-=0.01;
}
if(key == GLUT_KEY_F11)
{
c2+=0.01;
}
if(key == GLUT_KEY_F12)
{
c2-=0.01;
}
if(key == GLUT_KEY_F7)
{
g=g/2;
}
if(key == GLUT_KEY_F8)
{
g=g*2;
}
glutPostRedisplay();
}
void processNormalKeys(unsigned char key, int x, int y)
{
if (key == 27) exit(0);
}
int main(int argc, char ** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
glutInitWindowSize(dividecubesby,dividecubesby);
glutCreateWindow("Mandelbrot Set");
init();
glutDisplayFunc(display);
glutSpecialFunc(processSpecialKeys);
glutKeyboardFunc(processNormalKeys);
glutMainLoop();
return 0;
}

Answer 1

You're almost certainly running out of bits of precision - double has 53 bits, enough to zoom in to at most about 2^-43 or 1e-13 in a 1024px window - beyond that you don't even have enough bits to distinguish the C values for different pixels. This leads to grainy rectangles when you zoom in "too far".
You might look at libqd or libmpfr or other higher precision numerical libraries, which give you floating point with more bits. They're quite a lot slower though.