import javax.imageio.ImageIO;
import java.awt.*;
import java.awt.image.*;
import java.io.File;
import java.io.IOException;

class Main {
 static final int X = 512, Y = 512;
 static final int terms = 32;
 static final double pi = Math.PI;
 static final double t = pi/6;
 static final int colors[] =
    {0xffffff, 0xff00ff, 0xff80ff, 0xffff, 0x80ffff, 0xffff00};
 static final double coef[] = new double[terms];
 static BufferedImage I =
    new BufferedImage(X, Y, BufferedImage.TYPE_3BYTE_BGR);
 static double cos(double x) {return Math.cos(x);}
 static double clip(double x) {return x<-1?-1:x>1?1:x;}
 static void pl(int i, double y, int col) {
 I.setRGB(i, (int)((clip(-y*.7)+1)*Y/2), col);}

static public void main(String[] args){
  final int cm = colors.length;
  for(int j = 0; j<terms; ++j) {int k=2*j+1;
     coef[j] = (4/pi)*((j&1)>0?-1:1)*cos(t*k)/k;
     System.out.println(" a["+k+"] = "+coef[j]);}
for (int i = 0; i<X; ++i) {
   double x = i*(pi/X);
   double s = 0.;
   int color = 0;
   pl(i, x<(pi/2-t)?1:x<(pi/2+t)?0:-1, 0xffffff);
   for(int j = 0; j<terms; ++j) {
    int k = 2*j+1;
    s += cos(k*x)*coef[j];
    if(0==(k & (k+1))) // k = 2^z - 1
      try {pl(i, s, colors[(color++) % cm]);} catch (Exception ww) {
        System.out.println("i="+i+" j="+j+" s="+s+" x="+x);}}}

   Frame f = new Frame( "square wave" );
   f.add("Center", new MainCanvas());
   f.setSize(new Dimension(X,Y+22));
   f.setVisible(true);
   if(args.length > 0) try {
      File file = new File(args[0]);
      ImageIO.write(I, "png", file );}
   catch (IOException e) {System.err.println("image not saved.");}
}}

class MainCanvas extends Canvas{
    public void paint(Graphics g){
        g.drawImage(Main.I, 0, 0, Color.red, null);}}