##Java - 505 486 476 452 389
Just a standard calculation, with golfitude added.
Golfed:
public class M{public static void main(String[]v){int n=640,t,s,i=n,j;final BufferedImage z=new BufferedImage(n,n,1);JFrame f=new JFrame(){public void paint(Graphics g){g.drawImage(z,0,28,null);}};f.setSize(n,668);while(i-->0)for(j=0;j<n;z.setRGB(i,j++,(99-s)*9999)){double c=4d/n,a=c*i-2,b=c*j-2,r=a,e=b,p;for(s=t=0;t++<99&&r*r+e*e<4;s=t,p=r*r-e*e+a,e=r*e+e*r+b,r=p);}f.setVisible(1>0);}} With line breaks:
public class M{ public static void main(String[]v){ int n=640,t,s,i=n,j; final BufferedImage z=new BufferedImage(n,n,1); JFrame f=new JFrame(){ public void paint(Graphics g){ g.drawImage(z,0,28,null); } }; f.setSize(n,668); while(i-->0) for(j=0;j<n;z.setRGB(i,j++,(99-s)*9999)){ double c=4d/n,a=c*i-2,b=c*j-2,r=a,e=b,p; for(s=t=0;t++<99&&r*r+e*e<4;s=t,p=r*r-e*e+a,e=r*e+e*r+b,r=p); } f.setVisible(1>0); } } 