// Reflections inside Descartes' Folium.
// It should be ergodic but appears not to be.
import java.awt.*;
import java.awt.image.*;
import javax.imageio.ImageIO;
import java.io.File;
import java.io.IOException;
class Main {
static double c = 0;
static final int X = 750, Y = X;
static final double xm = X, e = 1.8;
static double p(double x, double y){return x*x*x+y*y*y-e*x*y;}
static double fx(double x, double y){return 3*x*x-e*y;}
static double fy(double x, double y){return 3*y*y-e*x;}
  static BufferedImage I = new BufferedImage(X, Y, BufferedImage.TYPE_INT_RGB);
  static Graphics g = I.getGraphics();
  static WritableRaster wr = I.getRaster();
  static void dr(double x, double y, double xe, double ye){
    g.drawLine((int)(x*xm), Y-1-(int)(y*xm), (int)(xe*xm), Y-1-(int)(ye*xm));};
static class MainCanvas extends Canvas {
   public void paint(Graphics g){g.drawImage(Main.I, 0, 0, Color.red, null);}}

static public void main( String[] args ){
  Frame f = new Frame("Ergodic Folium");
  Canvas can = new MainCanvas();
  f.add(can, "Center");
  f.setSize(new Dimension(X, Y));
  double x = 0.16, y = 0.5, xd = 1, yd = -0.3; c = p(x, y);
  f.setVisible(true);
  try {int[] mk = new int[] {255, 255, 255};
       for(int i = 0; i<X; ++i) for(int j = 0; j<Y; ++j) 
       if(p(i/xm, j/xm) > c) wr.setPixel(i, Y-1-j, mk);}
  catch (ArrayIndexOutOfBoundsException d) {System.out.println("zarg");}
  g.setColor(new Color((float)0.9, (float)0.5, (float)0.8));
  for (int q = 0; q<300; ++q)
  {double a = xd*xd*xd + yd*yd*yd, b = 3*(x*xd*xd + y*yd*yd) - e*xd*yd,
    z = (-b + Math.sqrt(b*b - 4*a*(3*(x*x*xd + y*y*yd) - e*(x*yd + y*xd))))/(2*a);
    double nx =  x+z*xd, ny = y+z*yd; dr(x, y, nx, ny);
    x = nx; y = ny;
    double px = fx(x, y), py = fy(x, y), r = 2*(xd*px + yd*py)/(px*px+py*py);
    xd -= r*px; yd -= r*py;
    System.out.println("z = "+ z + ", p = " + (p(x, y) - c)
    + ", px = "+px+", py = "+py);}
  for(int q=0; q < args.length; ++q) {int z = args[q].lastIndexOf('.');
      if (z > 0) try {ImageIO.write(I, args[q].substring(z+1), new File(args[q]));}
                 catch (IOException e) {System.err.println("image not saved.");}}
}}
/*
p(z) = p(x+z*xd, y+z*yd) = p(x, y)
  + 3*z*(x^2*xd + y^2*yd) + 3*z^2*(x*xd^2 + y*yd^2)
  + z^3*(xd^3 + yd^3) - e*(x*yd*z + xd*y*z + xd*yd*z^2)
= z*((xd^3 + yd*3)*z^2 + (3*(x*xd^2 + y*yd^2) - e*xd*yd)*z +
   3*(x^2*xd + y^2*yd) - e*(x*yd + xd*y))
a = (xd^3 + yd*3)
b = 3*(x*xd^2 + y*yd^2) - e*xd*yd
z = (-b +- sqrt(b^2 - 4*a*(3*(x^2*xd + y^2*yd) - e*(x*yd + xd*y))))/(2*a)
*/
/* zd -= 2*(zd.n)n/(|n|^2) */