recursion problem

[newbieha]

Hi,everyone Im new to JAVA and not sure how does recursion work in JAVA
I have to use JAVA Turtle to draw snowflake
here is the pseudocode.

procedure snowflakePart( S, N ) :
if N is greater than 0:
move turtle forward S units
if N is greater than 1:
# generate the 5 sub-branches of this snowflake part
turn turtle left 120 degrees
loop 5 times:
call snowflakePart( S/3, N-1 )
turn turtle right 60 degrees
turn turtle right 180 degrees
move turtle backward S units

procedure drawSnowflake( S, N ) :
loop 6 times:
call snowflakePart( S, N )
turn turtle left 60 degrees

public static void main(String[] args){
    	double x0 = 10;
    	double y0 = 10.0;
    	double a0 = 0.0;
    	Turtle turtle  = new Turtle(x0, y0, a0);
    	double S;
        double N;
        Scanner sc= new Scanner(System.in);
        System.out.print("Enter S: ");
        S=sc.nextInt();
        Scanner bc= new Scanner(System.in);
        System.out.print("Enter N: ");
        N=bc.nextInt();
        snowflake(S,N,turtle);
        }
    
        
    public static void snowflake(double S, double N,Turtle turtle){
    	if (N>0){
    		turtle.goForward(S); 	
        	if(N>1){
        		turtle.turnLeft(120);
        		for (int g=1; g<=5; g++){
        			snowflake(S/3,N-1,turtle);
        			turtle.turnRight(60);
        		}
        		turtle.turnRight(180);
        	}
    }
    	drawSnowflake(S, N,turtle);
}
    public static void drawSnowflake(double S, double N,Turtle turtle){
    	
    	for(int h=1; h<=6; h++){
    		snowflake(S, N,turtle);
    		turtle.turnLeft(60);
    	}
    	
    }

This is what I have so far. I also tried the pseudocode in python. I got it works fine.

here are the errors in JAVA.
at Turtle.drawSnowflake(Turtle.java:166)
at Turtle.snowflake(Turtle.java:161)
at Turtle.drawSnowflake(Turtle.java:166)
at Turtle.snowflake(Turtle.java:161)
at Turtle.drawSnowflake(Turtle.java:166)

Thanks.

[JamesCherrill]

When you get a Java error it comes with a complete description and a stack of line numbers. Please post the full details of your error(s). Also post the full source code - you post identifies the error as being on lines 161/166, but the code you posted only goes to line 39!
However, I did notice that your Java snowflake method calls drawSnowflake at the end, which is not in the pseudocode.
You also renamed snowflakePart to snowflake - makes no difference to the compiler, but may reveal something about how you are thinking of it, eg you call snowflake from main, but maybe that should be drawSnowflake?

[newbieha]

However, I did notice that your Java snowflake method calls drawSnowflake at the end, which is not in the pseudocode.

I think this is one way to pass the parameters to another function.I don't know how to pass the S and N to drawsnowflakes. and that is the method I googled

[newbieha]

You also renamed snowflakePart to snowflake - makes no difference to the compiler, but may reveal something about how you are thinking of it, eg you call snowflake from main, but maybe that should be drawSnowflake?

again, I don't mean to call the function in main. I tried to pass S and N from main to snowflake function

[newbieha]

/*************************************************************************
 *  Compilation:  javac StdDraw.java
 *  Execution:    java StdDraw
 *
 *  Standard drawing library. This class provides a basic capability for
 *  creating drawings with your programs. It uses a simple graphics model that
 *  allows you to create drawings consisting of points, lines, and curves
 *  in a window on your computer and to save the drawings to a file.
 *
 *  Todo
 *  ----
 *    -  Add support for gradient fill, etc.
 *
 *  Remarks
 *  -------
 *    -  don't use AffineTransform for rescaling since it inverts
 *       images and strings
 *    -  careful using setFont in inner loop within an animation -
 *       it can cause flicker
 *       
 *       Copyright 2007, Robert Sedgewick and Kevin Wayne. 
 *       
 *  Versions:
 *  	$Id$
 *  
 *  Revisions:
 *  	$Log$
 *
 *************************************************************************/

import java.io.*;
import java.net.*;
import java.awt.*;
import java.awt.geom.*;
import java.awt.event.*;
import java.awt.image.*;
import javax.swing.*;
import javax.imageio.ImageIO;
import java.util.LinkedList;

/**
 *  <i>Standard draw</i>. This class provides a basic capability for
 *  creating drawings with your programs. It uses a simple graphics model that
 *  allows you to create drawings consisting of points, lines, and curves
 *  in a window on your computer and to save the drawings to a file.
 *  <p>
 *  For additional documentation, see <a href="http://www.cs.princeton.edu/introcs/15inout">Section 1.5</a> of
 *  <i>Introduction to Programming in Java: An Interdisciplinary Approach</i> by Robert Sedgewick and Kevin Wayne.
 */
public final class StdDraw implements ActionListener, MouseListener, MouseMotionListener, KeyListener {

    // pre-defined colors
    public static final Color BLACK      = Color.BLACK;
    public static final Color BLUE       = Color.BLUE;
    public static final Color CYAN       = Color.CYAN;
    public static final Color DARK_GRAY  = Color.DARK_GRAY;
    public static final Color GRAY       = Color.GRAY;
    public static final Color GREEN      = Color.GREEN;
    public static final Color LIGHT_GRAY = Color.LIGHT_GRAY;
    public static final Color MAGENTA    = Color.MAGENTA;
    public static final Color ORANGE     = Color.ORANGE;
    public static final Color PINK       = Color.PINK;
    public static final Color RED        = Color.RED;
    public static final Color WHITE      = Color.WHITE;
    public static final Color YELLOW     = Color.YELLOW;
    public static final Color BOOK_BLUE  = new Color(9, 90, 166);   // Intro to Programming
    public static final Color BOOK_RED   = new Color(173, 32, 24);  // Algorithms 4

    // default colors
    private static final Color DEFAULT_PEN_COLOR   = BLACK;
    private static final Color DEFAULT_CLEAR_COLOR = WHITE;

    // current pen color
    private static Color penColor;

    // default canvas size is SIZE-by-SIZE
    private static final int DEFAULT_SIZE = 512;
    private static int width  = DEFAULT_SIZE;
    private static int height = DEFAULT_SIZE;

    // default pen radius
    private static final double DEFAULT_PEN_RADIUS = 0.002;

    // current pen radius
    private static double penRadius;

    // show we draw immediately or wait until next show?
    private static boolean defer = false;

    // boundary of drawing canvas, 5% border
    private static final double BORDER = 0.05;
    private static final double DEFAULT_XMIN = 0.0;
    private static final double DEFAULT_XMAX = 1.0;
    private static final double DEFAULT_YMIN = 0.0;
    private static final double DEFAULT_YMAX = 1.0;
    private static double xmin, ymin, xmax, ymax;

    // for synchronization
    private static Object mouseLock = new Object();
    private static Object keyLock = new Object();

    // default font
    private static final Font DEFAULT_FONT = new Font("SansSerif", Font.PLAIN, 16);

    // current font
    private static Font font;

    // double buffered graphics
    private static BufferedImage offscreenImage, onscreenImage;
    private static Graphics2D offscreen, onscreen;

    // singleton for callbacks: avoids generation of extra .class files
    private static StdDraw std = new StdDraw();

    // the frame for drawing to the screen
    private static JFrame frame;

    // mouse state
    private static boolean mousePressed = false;
    private static double mouseX = 0;
    private static double mouseY = 0;

    // keyboard state
    private static LinkedList<Character> keysTyped = new LinkedList<Character>();

    // not instantiable
    private StdDraw() { }


    // static initializer
    static { init(); }

    /**
     * Set the window size to w-by-h pixels.
     *
     * @param w the width as a number of pixels
     * @param h the height as a number of pixels
     * @throws a RunTimeException if the width or height is 0 or negative
     */
    public static void setCanvasSize(int w, int h) {
        if (w < 1 || h < 1) throw new RuntimeException("width and height must be positive");
        width = w;
        height = h;
        init();
    }

    // init
    private static void init() {
        if (frame != null) frame.setVisible(false);
        frame = new JFrame();
        offscreenImage = new BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB);
        onscreenImage  = new BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB);
        offscreen = offscreenImage.createGraphics();
        onscreen  = onscreenImage.createGraphics();
        setXscale();
        setYscale();
        offscreen.setColor(DEFAULT_CLEAR_COLOR);
        offscreen.fillRect(0, 0, width, height);
        setPenColor();
        setPenRadius();
        setFont();
        clear();

        // add antialiasing
        RenderingHints hints = new RenderingHints(RenderingHints.KEY_ANTIALIASING,
                                                  RenderingHints.VALUE_ANTIALIAS_ON);
        hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
        offscreen.addRenderingHints(hints);

        // frame stuff
        ImageIcon icon = new ImageIcon(onscreenImage);
        JLabel draw = new JLabel(icon);

        draw.addMouseListener(std);
        draw.addMouseMotionListener(std);

        frame.setContentPane(draw);
        frame.addKeyListener(std);    // JLabel cannot get keyboard focus
        frame.setResizable(false);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);            // closes all windows
        // frame.setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);      // closes only current window
        frame.setTitle("Standard Draw");
        frame.setJMenuBar(createMenuBar());
        frame.pack();
        frame.requestFocusInWindow();
        frame.setVisible(true);
    }

    // create the menu bar (changed to private)
    private static JMenuBar createMenuBar() {
        JMenuBar menuBar = new JMenuBar();
        JMenu menu = new JMenu("File");
        menuBar.add(menu);
        JMenuItem menuItem1 = new JMenuItem(" Save...   ");
        menuItem1.addActionListener(std);
        menuItem1.setAccelerator(KeyStroke.getKeyStroke(KeyEvent.VK_S,
                                Toolkit.getDefaultToolkit().getMenuShortcutKeyMask()));
        menu.add(menuItem1);
        return menuBar;
    }


   /*************************************************************************
    *  User and screen coordinate systems
    *************************************************************************/
    
    /**
     * Set the window title.
     * 
     * @param title The window title.
     */
    public static void setTitle(String title) { frame.setTitle(title); }

    /**
     * Set the x-scale to be the default (between 0.0 and 1.0).
     */
    public static void setXscale() { setXscale(DEFAULT_XMIN, DEFAULT_XMAX); }

    /**
     * Set the y-scale to be the default (between 0.0 and 1.0).
     */
    public static void setYscale() { setYscale(DEFAULT_YMIN, DEFAULT_YMAX); }

    /**
     * Set the x-scale (a 10% border is added to the values)
     * @param min the minimum value of the x-scale
     * @param max the maximum value of the x-scale
     */
    public static void setXscale(double min, double max) {
        double size = max - min;
        xmin = min - BORDER * size;
        xmax = max + BORDER * size;
    }

    /**
     * Set the y-scale (a 10% border is added to the values).
     * @param min the minimum value of the y-scale
     * @param max the maximum value of the y-scale
     */
    public static void setYscale(double min, double max) {
        double size = max - min;
        ymin = min - BORDER * size;
        ymax = max + BORDER * size;
    }

    // helper functions that scale from user coordinates to screen coordinates and back
    private static double  scaleX(double x) { return width  * (x - xmin) / (xmax - xmin); }
    private static double  scaleY(double y) { return height * (ymax - y) / (ymax - ymin); }
    private static double factorX(double w) { return w * width  / Math.abs(xmax - xmin);  }
    private static double factorY(double h) { return h * height / Math.abs(ymax - ymin);  }
    private static double   userX(double x) { return xmin + x * (xmax - xmin) / width;    }
    private static double   userY(double y) { return ymax - y * (ymax - ymin) / height;   }


    /**
     * Clear the screen to the default color (white).
     */
    public static void clear() { clear(DEFAULT_CLEAR_COLOR); }
    /**
     * Clear the screen to the given color.
     * @param color the Color to make the background
     */
    public static void clear(Color color) {
        offscreen.setColor(color);
        offscreen.fillRect(0, 0, width, height);
        offscreen.setColor(penColor);
        draw();
    }

    /**
     * Set the pen size to the default (.002).
     */
    public static void setPenRadius() { setPenRadius(DEFAULT_PEN_RADIUS); }
    /**
     * Set the radius of the pen to the given size.
     * @param r the radius of the pen
     * @throws RuntimeException if r is negative
     */
    public static void setPenRadius(double r) {
        if (r < 0) throw new RuntimeException("pen radius must be positive");
        penRadius = r * DEFAULT_SIZE;
        // BasicStroke stroke = new BasicStroke((float) penRadius, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND);
        BasicStroke stroke = new BasicStroke((float) penRadius);
        offscreen.setStroke(stroke);
    }

    /**
     * Set the pen color to the default color (black).
     */
    public static void setPenColor() { setPenColor(DEFAULT_PEN_COLOR); }
    /**
     * Set the pen color to the given color. The available pen colors are
     * BLACK, BLUE, CYAN, DARK_GRAY, GRAY, GREEN, LIGHT_GRAY, MAGENTA,
     * ORANGE, PINK, RED, WHITE, and YELLOW.
     * @param color the Color to make the pen
     */
    public static void setPenColor(Color color) {
        penColor = color;
        offscreen.setColor(penColor);
    }

    /**
     * Set the font to the default font (sans serif, 16 point).
     */
    public static void setFont() { setFont(DEFAULT_FONT); }

    /**
     * Set the font to the given value.
     * @param f the font to make text
     */
    public static void setFont(Font f) { font = f; }


   /*************************************************************************
    *  Drawing geometric shapes.
    *************************************************************************/

    /**
     * Draw a line from (x0, y0) to (x1, y1).
     * @param x0 the x-coordinate of the starting point
     * @param y0 the y-coordinate of the starting point
     * @param x1 the x-coordinate of the destination point
     * @param y1 the y-coordinate of the destination point
     */
    public static void line(double x0, double y0, double x1, double y1) {
        offscreen.draw(new Line2D.Double(scaleX(x0), scaleY(y0), scaleX(x1), scaleY(y1)));
        draw();
    }

    /**
     * Draw one pixel at (x, y).
     * @param x the x-coordinate of the pixel
     * @param y the y-coordinate of the pixel
     */
    private static void pixel(double x, double y) {
        offscreen.fillRect((int) Math.round(scaleX(x)), (int) Math.round(scaleY(y)), 1, 1);
    }

    /**
     * Draw a point at (x, y).
     * @param x the x-coordinate of the point
     * @param y the y-coordinate of the point
     */
    public static void point(double x, double y) {
        double xs = scaleX(x);
        double ys = scaleY(y);
        double r = penRadius;
        // double ws = factorX(2*r);
        // double hs = factorY(2*r);
        // if (ws <= 1 && hs <= 1) pixel(x, y);
        if (r <= 1) pixel(x, y);
        else offscreen.fill(new Ellipse2D.Double(xs - r/2, ys - r/2, r, r));
        draw();
    }

    /**
     * Draw a circle of radius r, centered on (x, y).
     * @param x the x-coordinate of the center of the circle
     * @param y the y-coordinate of the center of the circle
     * @param r the radius of the circle
     * @throws RuntimeException if the radius of the circle is negative
     */
    public static void circle(double x, double y, double r) {
        if (r < 0) throw new RuntimeException("circle radius can't be negative");
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*r);
        double hs = factorY(2*r);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.draw(new Ellipse2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draw filled circle of radius r, centered on (x, y).
     * @param x the x-coordinate of the center of the circle
     * @param y the y-coordinate of the center of the circle
     * @param r the radius of the circle
     * @throws RuntimeException if the radius of the circle is negative
     */
    public static void filledCircle(double x, double y, double r) {
        if (r < 0) throw new RuntimeException("circle radius can't be negative");
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*r);
        double hs = factorY(2*r);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.fill(new Ellipse2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draw an arc of radius r, centered on (x, y), from angle1 to angle2 (in degrees).
     * @param x the x-coordinate of the center of the circle
     * @param y the y-coordinate of the center of the circle
     * @param r the radius of the circle
     * @param angle1 the starting angle. 0 would mean an arc beginning at 3 o'clock.
     * @param angle2 the angle at the end of the arc. For example, if
     *        you want a 90 degree arc, then angle2 should be angle1 + 90.
     * @throws RuntimeException if the radius of the circle is negative
     */
    public static void arc(double x, double y, double r, double angle1, double angle2) {
        if (r < 0) throw new RuntimeException("arc radius can't be negative");
        while (angle2 < angle1) angle2 += 360;
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*r);
        double hs = factorY(2*r);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.draw(new Arc2D.Double(xs - ws/2, ys - hs/2, ws, hs, angle1, angle2 - angle1, Arc2D.OPEN));
        draw();
    }

    /**
     * Draw a square of side length 2r, centered on (x, y).
     * @param x the x-coordinate of the center of the square
     * @param y the y-coordinate of the center of the square
     * @param r radius is half the length of any side of the square
     * @throws RuntimeException if r is negative
     */
    public static void square(double x, double y, double r) {
        if (r < 0) throw new RuntimeException("square side length can't be negative");
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*r);
        double hs = factorY(2*r);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.draw(new Rectangle2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draw a filled square of side length 2r, centered on (x, y).
     * @param x the x-coordinate of the center of the square
     * @param y the y-coordinate of the center of the square
     * @param r radius is half the length of any side of the square
     * @throws RuntimeException if r is negative
     */
    public static void filledSquare(double x, double y, double r) {
        if (r < 0) throw new RuntimeException("square side length can't be negative");
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(2*r);
        double hs = factorY(2*r);
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else offscreen.fill(new Rectangle2D.Double(xs - ws/2, ys - hs/2, ws, hs));
        draw();
    }

    /**
     * Draw a polygon with the given (x[i], y[i]) coordinates.
     * @param x an array of all the x-coordindates of the polygon
     * @param y an array of all the y-coordindates of the polygon
     */
    public static void polygon(double[] x, double[] y) {
        int N = x.length;
        GeneralPath path = new GeneralPath();
        path.moveTo((float) scaleX(x[0]), (float) scaleY(y[0]));
        for (int i = 0; i < N; i++)
            path.lineTo((float) scaleX(x[i]), (float) scaleY(y[i]));
        path.closePath();
        offscreen.draw(path);
        draw();
    }

    /**
     * Draw a filled polygon with the given (x[i], y[i]) coordinates.
     * @param x an array of all the x-coordindates of the polygon
     * @param y an array of all the y-coordindates of the polygon
     */
    public static void filledPolygon(double[] x, double[] y) {
        int N = x.length;
        GeneralPath path = new GeneralPath();
        path.moveTo((float) scaleX(x[0]), (float) scaleY(y[0]));
        for (int i = 0; i < N; i++)
            path.lineTo((float) scaleX(x[i]), (float) scaleY(y[i]));
        path.closePath();
        offscreen.fill(path);
        draw();
    }



   /*************************************************************************
    *  Drawing images.
    *************************************************************************/

    // get an image from the given filename
    private static Image getImage(String filename) {

        // to read from file
        ImageIcon icon = new ImageIcon(filename);

        // try to read from URL
        if ((icon == null) || (icon.getImageLoadStatus() != MediaTracker.COMPLETE)) {
            try {
                URL url = new URL(filename);
                icon = new ImageIcon(url);
            } catch (Exception e) { /* not a url */ }
        }

        // in case file is inside a .jar
        if ((icon == null) || (icon.getImageLoadStatus() != MediaTracker.COMPLETE)) {
            URL url = StdDraw.class.getResource(filename);
            if (url == null) throw new RuntimeException("image " + filename + " not found");
            icon = new ImageIcon(url);
        }

        return icon.getImage();
    }

    /**
     * Draw picture (gif, jpg, or png) centered on (x, y).
     * @param x the center x-coordinate of the image
     * @param y the center y-coordinate of the image
     * @param s the name of the image/picture, e.g., "ball.gif"
     * @throws RuntimeException if the image is corrupt
     */
    public static void picture(double x, double y, String s) {
        Image image = getImage(s);
        double xs = scaleX(x);
        double ys = scaleY(y);
        int ws = image.getWidth(null);
        int hs = image.getHeight(null);
        if (ws < 0 || hs < 0) throw new RuntimeException("image " + s + " is corrupt");

        offscreen.drawImage(image, (int) Math.round(xs - ws/2.0), (int) Math.round(ys - hs/2.0), null);
        draw();
    }

    /**
     * Draw picture (gif, jpg, or png) centered on (x, y),
     * rotated given number of degrees
     * @param x the center x-coordinate of the image
     * @param y the center y-coordinate of the image
     * @param s the name of the image/picture, e.g., "ball.gif"
     * @param degrees is the number of degrees to rotate counterclockwise
     * @throws RuntimeException if the image is corrupt
     */
    public static void picture(double x, double y, String s, double degrees) {
        Image image = getImage(s);
        double xs = scaleX(x);
        double ys = scaleY(y);
        int ws = image.getWidth(null);
        int hs = image.getHeight(null);
        if (ws < 0 || hs < 0) throw new RuntimeException("image " + s + " is corrupt");

        offscreen.rotate(Math.toRadians(-degrees), xs, ys);
        offscreen.drawImage(image, (int) Math.round(xs - ws/2.0), (int) Math.round(ys - hs/2.0), null);
        offscreen.rotate(Math.toRadians(+degrees), xs, ys);

        draw();
    }

    /**
     * Draw picture (gif, jpg, or png) centered on (x, y), rescaled to w-by-h.
     * @param x the center x coordinate of the image
     * @param y the center y coordinate of the image
     * @param s the name of the image/picture, e.g., "ball.gif"
     * @param w the width of the image
     * @param h the height of the image
     * @throws RuntimeException if the width height are negative
     * @throws RuntimeException if the image is corrupt
     */
    public static void picture(double x, double y, String s, double w, double h) {
        Image image = getImage(s);
        double xs = scaleX(x);
        double ys = scaleY(y);
        if (w < 0) throw new RuntimeException("width is negative: " + w);
        if (h < 0) throw new RuntimeException("height is negative: " + h);
        double ws = factorX(w);
        double hs = factorY(h);
        if (ws < 0 || hs < 0) throw new RuntimeException("image " + s + " is corrupt");
        if (ws <= 1 && hs <= 1) pixel(x, y);
        else {
            offscreen.drawImage(image, (int) Math.round(xs - ws/2.0),
                                       (int) Math.round(ys - hs/2.0),
                                       (int) Math.round(ws),
                                       (int) Math.round(hs), null);
        }
        draw();
    }


    /**
     * Draw picture (gif, jpg, or png) centered on (x, y), rotated
     * given number of degrees, rescaled to w-by-h.
     * @param x the center x-coordinate of the image
     * @param y the center y-coordinate of the image
     * @param s the name of the image/picture, e.g., "ball.gif"
     * @param w the width of the image
     * @param h the height of the image
     * @param degrees is the number of degrees to rotate counterclockwise
     * @throws RuntimeException if the image is corrupt
     */
    public static void picture(double x, double y, String s, double w, double h, double degrees) {
        Image image = getImage(s);
        double xs = scaleX(x);
        double ys = scaleY(y);
        double ws = factorX(w);
        double hs = factorY(h);
        if (ws < 0 || hs < 0) throw new RuntimeException("image " + s + " is corrupt");
        if (ws <= 1 && hs <= 1) pixel(x, y);

        offscreen.rotate(Math.toRadians(-degrees), xs, ys);
        offscreen.drawImage(image, (int) Math.round(xs - ws/2.0),
                                   (int) Math.round(ys - hs/2.0),
                                   (int) Math.round(ws),
                                   (int) Math.round(hs), null);
        offscreen.rotate(Math.toRadians(+degrees), xs, ys);

        draw();
    }


   /*************************************************************************
    *  Drawing text.
    *************************************************************************/

    /**
     * Write the given text string in the current font, centered on (x, y).
     * @param x the center x-coordinate of the text
     * @param y the center y-coordinate of the text
     * @param s the text
     */
    public static void text(double x, double y, String s) {
        offscreen.setFont(font);
        FontMetrics metrics = offscreen.getFontMetrics();
        double xs = scaleX(x);
        double ys = scaleY(y);
        int ws = metrics.stringWidth(s);
        int hs = metrics.getDescent();
        offscreen.drawString(s, (float) (xs - ws/2.0), (float) (ys + hs));
        draw();
    }

    /**
     * Write the given text string in the current font, left-aligned at (x, y).
     * @param x the x-coordinate of the text
     * @param y the y-coordinate of the text
     * @param s the text
     */
    public static void textLeft(double x, double y, String s) {
        offscreen.setFont(font);
        FontMetrics metrics = offscreen.getFontMetrics();
        double xs = scaleX(x);
        double ys = scaleY(y);
        //int ws = metrics.stringWidth(s);
        int hs = metrics.getDescent();
        offscreen.drawString(s, (float) (xs), (float) (ys + hs));
        show();
    }

    /**
     * Write the given text string in the current font, right-aligned at (x, y).
     * @param x the x-coordinate of the text
     * @param y the y-coordinate of the text
     * @param s the text
     */
    public static void textRight(double x, double y, String s) {
        offscreen.setFont(font);
        FontMetrics metrics = offscreen.getFontMetrics();
        double xs = scaleX(x);
        double ys = scaleY(y);
        int ws = metrics.stringWidth(s);
        int hs = metrics.getDescent();
        offscreen.drawString(s, (float) (xs - ws), (float) (ys + hs));
        show();
    }



    /**
     * Display on screen, pause for t milliseconds, and turn on
     * <em>animation mode</em>: subsequent calls to
     * drawing methods such as <tt>line()</tt>, <tt>circle()</tt>, and <tt>square()</tt>
     * will not be displayed on screen until the next call to <tt>show()</tt>.
     * This is useful for producing animations (clear the screen, draw a bunch of shapes,
     * display on screen for a fixed amount of time, and repeat). It also speeds up
     * drawing a huge number of shapes (call <tt>show(0)</tt> to defer drawing
     * on screen, draw the shapes, and call <tt>show(0)</tt> to display them all
     * on screen at once).
     * @param t number of milliseconds
     */
    public static void show(int t) {
        defer = false;
        draw();
        try { Thread.sleep(t); }
        catch (InterruptedException e) { System.out.println("Error sleeping"); }
        defer = true;
    }


    /**
     * Display on-screen and turn off animation mode:
     * subsequent calls to
     * drawing methods such as <tt>line()</tt>, <tt>circle()</tt>, and <tt>square()</tt>
     * will be displayed on screen when called. This is the default.
     */
    public static void show() {
        defer = false;
        draw();
    }

    // draw onscreen if defer is false
    private static void draw() {
        if (defer) return;
        onscreen.drawImage(offscreenImage, 0, 0, null);
        frame.repaint();
    }


   /*************************************************************************
    *  Save drawing to a file.
    *************************************************************************/

    /**
     * Save to file - suffix must be png, jpg, or gif.
     * @param filename the name of the file with one of the required suffixes
     */
    public static void save(String filename) {
        File file = new File(filename);
        String suffix = filename.substring(filename.lastIndexOf('.') + 1);

        // png files
        if (suffix.toLowerCase().equals("png")) {
            try { ImageIO.write(offscreenImage, suffix, file); }
            catch (IOException e) { e.printStackTrace(); }
        }

        // need to change from ARGB to RGB for jpeg
        // reference: http://archives.java.sun.com/cgi-bin/wa?A2=ind0404&L=java2d-interest&D=0&P=2727
        else if (suffix.toLowerCase().equals("jpg")) {
            WritableRaster raster = offscreenImage.getRaster();
            WritableRaster newRaster;
            newRaster = raster.createWritableChild(0, 0, width, height, 0, 0, new int[] {0, 1, 2});
            DirectColorModel cm = (DirectColorModel) offscreenImage.getColorModel();
            DirectColorModel newCM = new DirectColorModel(cm.getPixelSize(),
                                                          cm.getRedMask(),
                                                          cm.getGreenMask(),
                                                          cm.getBlueMask());
            BufferedImage rgbBuffer = new BufferedImage(newCM, newRaster, false,  null);
            try { ImageIO.write(rgbBuffer, suffix, file); }
            catch (IOException e) { e.printStackTrace(); }
        }

        else {
            System.out.println("Invalid image file type: " + suffix);
        }
    }


    /**
     * This method cannot be called directly.
     */
    public void actionPerformed(ActionEvent e) {
        FileDialog chooser = new FileDialog(StdDraw.frame, "Use a .png or .jpg extension", FileDialog.SAVE);
        chooser.setVisible(true);
        String filename = chooser.getFile();
        if (filename != null) {
            StdDraw.save(chooser.getDirectory() + File.separator + chooser.getFile());
        }
    }


   /*************************************************************************
    *  Mouse interactions.
    *************************************************************************/

    /**
     * Is the mouse being pressed?
     * @return true or false
     */
    public static boolean mousePressed() {
        synchronized (mouseLock) {
            return mousePressed;
        }
    }

    /**
     * What is the x-coordinate of the mouse?
     * @return the value of the x-coordinate of the mouse
     */
    public static double mouseX() {
        synchronized (mouseLock) {
            return mouseX;
        }
    }

    /**
     * What is the y-coordinate of the mouse?
     * @return the value of the y-coordinate of the mouse
     */
    public static double mouseY() {
        synchronized (mouseLock) {
            return mouseY;
        }
    }


    /**
     * This method cannot be called directly.
     */
    public void mouseClicked(MouseEvent e) { }

    /**
     * This method cannot be called directly.
     */
    public void mouseEntered(MouseEvent e) { }

    /**
     * This method cannot be called directly.
     */
    public void mouseExited(MouseEvent e) { }

    /**
     * This method cannot be called directly.
     */
    public void mousePressed(MouseEvent e) {
        synchronized (mouseLock) {
            mouseX = StdDraw.userX(e.getX());
            mouseY = StdDraw.userY(e.getY());
            mousePressed = true;
        }
    }

    /**
     * This method cannot be called directly.
     */
    public void mouseReleased(MouseEvent e) {
        synchronized (mouseLock) {
            mousePressed = false;
        }
    }

    /**
     * This method cannot be called directly.
     */
    public void mouseDragged(MouseEvent e)  {
        synchronized (mouseLock) {
            mouseX = StdDraw.userX(e.getX());
            mouseY = StdDraw.userY(e.getY());
        }
    }

    /**
     * This method cannot be called directly.
     */
    public void mouseMoved(MouseEvent e) {
        synchronized (mouseLock) {
            mouseX = StdDraw.userX(e.getX());
            mouseY = StdDraw.userY(e.getY());
        }
    }


   /*************************************************************************
    *  Keyboard interactions.
    *************************************************************************/

    /**
     * Has the user typed a key?
     * @return true if the user has typed a key, false otherwise
     */
    public static boolean hasNextKeyTyped() {
        synchronized (keyLock) {
            return !keysTyped.isEmpty();
        }
    }

    /**
     * What is the next key that was typed by the user?
     * @return the next key typed
     */
    public static char nextKeyTyped() {
        synchronized (keyLock) {
            return keysTyped.removeLast();
        }
    }

    /**
     * This method cannot be called directly.
     */
    public void keyTyped(KeyEvent e) {
        synchronized (keyLock) {
            keysTyped.addFirst(e.getKeyChar());
        }
    }

    /**
     * This method cannot be called directly.
     */
    public void keyPressed(KeyEvent e) { }

    /**
     * This method cannot be called directly.
     */
    public void keyReleased(KeyEvent e) { }




    /**
     * Test client.
     */
    public static void main(String[] args) {
        StdDraw.square(.2, .8, .1);
        StdDraw.filledSquare(.8, .8, .2);
        StdDraw.circle(.8, .2, .2);

        StdDraw.setPenColor(StdDraw.MAGENTA);
        StdDraw.setPenRadius(.02);
        StdDraw.arc(.8, .2, .1, 200, 45);

        // draw a blue diamond
        StdDraw.setPenRadius();
        StdDraw.setPenColor(StdDraw.BLUE);
        double[] x = { .1, .2, .3, .2 };
        double[] y = { .2, .3, .2, .1 };
        StdDraw.filledPolygon(x, y);

        // text
        StdDraw.setPenColor(StdDraw.BLACK);
        StdDraw.text(0.2, 0.5, "black text");
        StdDraw.setPenColor(StdDraw.WHITE);
        StdDraw.text(0.8, 0.8, "white text");
    }

}

Generated by GNU enscript 1.6.3.
[U][/U]

[newbieha]

/*************************************************************************
 *  Compilation:  javac Turtle.java
 *  Execution:    java Turtle
 *
 *  Data type for turtle graphics using standard draw.
 *  
 *  Copyright 2007, Robert Sedgewick and Kevin Wayne. 
 *  
 *  Version:
 *  	$Id$
 *  
 *  Revisions:
 *  	$Log$
 *
 *************************************************************************/

import java.awt.Color;

/**
 * A turtle graphics library built on StdDraw.
 * 
 * @author Robert Sedgewick, Kevin Wayne
 */
public class Turtle {
    private double x, y;     // turtle is at (x, y)
    private double angle;    // facing this many degrees counterclockwise from the x-axis

    /**
     * Construct the Turtle object.
     * 
     * @param x0 The starting x-coordinate for the turtle.
     * @param y0 The starting y-coordinate for the turtle.
     * @param a0 The degrees facing counterclockwise from the x-axis
     */
    public Turtle(double x0, double y0, double a0) {
        x = x0;
        y = y0;
        angle = a0;
    }
    
    /**
     * Set the user-defined coordinate system.
     * 
     * @param x0 The x-coordinate of the lower left corner of canvas.
     * @param y0 The y-coordinate of the lower left corner of canvas.
     * @param x1 The x-coordinate of the upper right corner of canvas.
     * @param y1 The y-coordinate of the upper right corner of canvas.
     */
    public void setWorldCoordinates(double x0, double y0, double x1, double y1) {
    	StdDraw.setXscale(x0, x1);
    	StdDraw.setYscale(y0, y1);
    }

    /**
     * Turn the turtle left.
     * 
     * @param delta The rotate orientation delta in degrees counterclockwise.
     */
    public void turnLeft(double delta) {
        angle += delta;
    }
    
    /**
     * Turn the turtle right.
     * 
     * @param delta The rotate orientation delta in degrees clockwise.
     */    
    public void turnRight(double delta) {
        angle -= delta;
    }

    /**
     * Move the turtle forward.
     * 
     * @param step The amount to move forward with the pen down.
     */
    public void goForward(double step) {
        double oldx = x;
        double oldy = y;
        x += step * Math.cos(Math.toRadians(angle));
        y += step * Math.sin(Math.toRadians(angle));
        StdDraw.line(oldx, oldy, x, y);
    }

    /**
     * Pause the turtle from drawing.
     * 
     * @param t The amount in milliseconds to pause the turtle.
     */
    public void pause(int t) {
        StdDraw.show(t);
    }

    /**
     * Set the turtle's pen color.
     * 
     * @param color The pen color.
     */
    public void setPenColor(Color color) {
        StdDraw.setPenColor(color);
    }

    /**
     * Set the thickness of the turtle's pen.
     * 
     * @param radius The dot thickness.
     */
    public void setPenRadius(double radius) {
        StdDraw.setPenRadius(radius);
    }

    /**
     * Set the canvas size.
     * 
     * @param width The canvas width.
     * @param height The canvas height.
     */
    public void setCanvasSize(int width, int height) {
        StdDraw.setCanvasSize(width, height);
    }
    
    /**
     * Set the canvas title.
     * 
     * @param title The canvas title.
     */
    public void setCanvasTitle(String title) {
    	StdDraw.setTitle(title);
    }

    // sample client for testing
    public static void main(String[] args) {
        double x0 = 0.5;
        double y0 = 0.0;
        double a0 = 60.0;
        double step = Math.sqrt(3)/2;
        Turtle turtle  = new Turtle(x0, y0, a0);
        turtle.goForward(step);
        turtle.turnLeft(120.0);
        turtle.goForward(step);
        turtle.turnLeft(120.0);
        turtle.goForward(step);
        turtle.turnLeft(120.0);
    }
}

Generated by GNU enscript 1.6.3.

here are two classes that provided.
use the Turtle class to draw the image.

[JamesCherrill]

I don't have time right now to check all your code, but it looks to me like your main should call drawSnowflake (passing N ans S as parameters), and drawSnowflake should call snowflakePart ( AKA snowflake ), but not vice-versa.

[mKorbel]

hmmm Jindent is very powerfull code formatter

to OP what's/are hint(s) about error by returns your IDE, I think that Robert has detailed examples, licence and TOC too on your pages, isn't it

[newbieha]

Thank you very much James. I edited the code as you said above and its working now