Lorenz.java

Below is the syntax highlighted version of Lorenz.java from §1.5 Input and Output.

/******************************************************************************
 *  Compilation:  javac Lorenz.java
 *  Execution:    java Lorenz
 *  Dependencies: StdDraw.java
 *
 *  Plot phase space (x vs. z) of Lorenz attractor with give set
 *  of initial conditions. Uses Euler's method to numerically
 *  approximate the answer.
 *
 ******************************************************************************/

public class Lorenz {

    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) {
        double x = 0.0, y = 20.0, z = 25.0;
        double dt = 0.001;

        StdDraw.clear(StdDraw.LIGHT_GRAY);
        StdDraw.setXscale(-25, 25);
        StdDraw.setXscale(0, 50);
        StdDraw.enableDoubleBuffering();


        // Use Euler's method to numerically solve ODE
        for (int i = 0; i < 50000; i++) {

            // update using Euler's method
            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;

            // draw
            StdDraw.setPenColor(StdDraw.BLUE);
            StdDraw.point(x, z);
            if (i % 10 == 0) {
                StdDraw.show();
                StdDraw.pause(10);
            }
        }
    }

}