// Lorenz.java
// Robert Sedgewick and Kevin Wayne
// Slightly reformatted by Andrew Davison, Nov. 2022

/* Plot phase space (x vs. z) of Lorenz attractor with one set of
   initial conditions and another set of slightly perturbed intial
   conditions. Uses Euler method.

   Usage:
     > compile Lorenz.java
     > run Lorenz
*/

import java.awt.Color;


public class Lorenz
{
  private double x, y, z;
  private Color color;

  public Lorenz(double x, double y, double z, Color color)
  {
    this.x = x;
    this.y = y;
    this.z = z;
    this.color = color;
  }


  public void update(double dt)
  {
    double xnew = x + dx(x, y, z) * dt;
    double ynew = y + dy(x, y, z) * dt;
    double znew = z + dz(x, y, z) * dt;
    x = xnew;
    y = ynew;
    z = znew;
  } /* update */


  public void draw()
  {
    StdDraw.setPenColor(color);
    StdDraw.point(x, z);
  }


  public static double dx(double x, double y, double z)
  {  return -10*(x - y);  }

  public static double dy(double x, double y, double z)
  {  return -x*z + 28*x - y;  }

  public static double dz(double x, double y, double z)
  {  return x*y - 8*z/3;  }


  // ------------------------------------------

  public static void main(String[] args)
  {
    StdDraw.setXscale(-25, 25);
    StdDraw.setYscale(  0, 50);

    Lorenz lorenz1 = new Lorenz(0.0, 20.00, 25.0, StdDraw.BLUE);
    Lorenz lorenz2 = new Lorenz(0.0, 20.01, 25.0, StdDraw.MAGENTA);

    // Use Euler's method to numerically solve ODE
    double dt = 0.001;
    for (int i = 0; i < 50000; i++) {
      lorenz1.update(dt);
      lorenz2.update(dt);
      lorenz1.draw();
      lorenz2.draw();
    }

    System.out.println("Drawing finished");
  } /* main */


}  // end of Lorenz class