Making a logarithmic spiral in Java

Question

import java.io.*;
import java.awt.*;

// Logarithmic spiral example
public class Spiral extends Frame
{// The spiral consists of n line segments. Line segment 1
// has starting point (hc, vc). Line segment k, for 1<=k<=n,
// has length k*d. Each line segment makes an angle of turn
// degrees with the previous line segment. The colors of the
// lines alternate between red, blue, and green.

final static int hc= 500;   // Center of spiral is (hc,vc)
final static int vc= 350;
final static int n= 2;    // Number of sides to draw
final static int turn= 45;  // The turn factor
final static double d= 1;   // Length of leg k is k*d

public void paint(Graphics g)
    {int h= hc;
    int v= vc;
    int k= 1;
    //Invariant: legs 1..k-1 have been drawn, and leg k is
    //           to be drawn with start point (hc,vc)
    while (k<=n)
        {//Draw line k
            if (k%3==0) g.setColor(Color.red);
            if (k%3==1) g.setColor(Color.blue);
            if (k%3==2) g.setColor(Color.green);

            int theta= k*turn %360;
            double L= k*d;
            // Calculate the end point (h_next,v_next) of
            // the line
                int h_next= (int) Math.round(
                        h+L*Math.cos(theta*Math.PI/180));
                int v_next= (int) Math.round(
                        v+L*Math.sin(theta*Math.PI/180));
            g.drawLine(h,v,h_next, v_next);

        h= h_next; v= v_next;
        k= k+1;
        }
    }

}

public class spiralMain {

public static void main(String args[]) {
            Spiral d = new Spiral();
    d.resize(10,10);
    d.move(0,50);
    d.setTitle("Logarithmic spiral");
    d.show();
    d.toFront();
    }
}

I'm attempting to create a logarithmic spiral using line segments. When I compile the code I get this:

But I'm trying to get something with a lot less lines. It should look something like this:

I'm not sure what I should change the values to in order to get it to that point.

Answer 1

If I remember correctly, you should set d to the golden ratio:

/**
 * Length of leg k is k * D
 */
private final static double D = 1.618;