hi i am a novice to c++ and have been doodling with borland graphics interface with dev 4.9.9.1

below is a programme i have written which calculates the mandelbrot set (all complex number c such that |z(k)| remained bounded subject to endless iteration z(n+1)=(z(n))^2+c, z(0)=c)).

Code:

#include <iostream.h>
#include <stdlib.h>
#include <winbgim.h>
int main(){
initwindow(800,600);
for(int x=0; x<=800; x++)
{
for(int y=0; y<=600; y++)
{
long double x_re = -2.0 + x*0.005;
long double y_im = 1.5 - y*0.005;
long double x_0 = x_re, y_0 = y_im;
short terminating=0, i=0;
do{
x_0=(x_0*x_0-y_0*y_0+x_re);
y_0=(2.0*x_0*y_0+y_im);
terminating++;
if(x_0*x_0+y_0*y_0>4.0){
i=1; break;
}
}while(terminating<1000);
if(i) continue;
else putpixel(x,y,1);
}
}
while(!kbhit());
closegraph();
return 0;
}

the problem with it is that when the graphics is generated, it looks like the mandelbrot set, but a grossly inaccurate representation. my guess is the limited number of significant figures c++ truncates for each calculation. any idea on increasing the number of significant figures? (something like what Window's calculator is capable of) thanks 4 the assistance!