Science and Computers I -- PHY307/607

Plotting points and lines in Java

• Login to SUnix and go to your PHY307 directory (type cd public_html/PHY307). Create a new directory with the command mkdir Simple2. Change its permissions with the command chmod 755 Simple2. Now execute the command cp Simple/*.java Simple2. This copies all the .java files in your old subdirectory Simple to the new subdirectory Simple2.
• Change to this new directory by typing cd Simple2. Rename the file Simple.java by typing mv Simple.java Simple2.java. Create a new .html file by typing pico Simple2.html. Inside this put the line of code

  
  < applet code=Simple2.class height=300 width=300 > < /applet >
  

• You now have set up everything so that you can create a new version of the Simple Applet which will be called Simple2 and will (hopefully) illustrate new features of Java.
• Make sure you are in the subdirectory Simple2 (if you type pwd you should get a line which ends in Simple2). If you are in public_html just type cd PHY307/Simple2 to enter the Simple2 subdirectory.
• Edit Simple2.java (type pico Simple2.java). First change the name Simple on the second line to Simple2.
• Under the line private Button mybutton; add the line

  private int counter=0;

  This defines a new variable which will count the number of times the iterate button has been clicked.
• To store the coordinates of the points produced by the map we need to use some arrays or lists. A list called x is denoted x[]. The first element of that list is denoted x[1], the second x[2] etc.
• Directly under the previous line defining the counter variable add the line

  
  private int x[],y[];

• This line defines the lists/arrays of integers x,y. To create them we need to use the new operator. Inside the init() method (after the add(mybutton) line) type the code

  x = new int[100];
  y = new int[100];
  

  This reserves space for 100 elements in each list or array. Also in init() replace the number 2.5 in the method call setA(2.5) by 3.75.
• OK, look at the paint() method. Delete the line involving the method drawString() (since we will now be drawing points to the screen rather than printing them out). In its place add the line

  
  for(int i=0;i < counter-1;i++)
  g.drawLine(x[i],y[i],x[i+1],y[i+1]);
  

  This draws lines between successive pairs of (x,y) coordinate points which are stored in the arrays x[] and y[]. The for loop runs progressively through all values of the integer variable i drawing a new bit of line between successive points indexed by i until you cover all pairs of points (limit is counter). The code fragment i++ adds 1 to i.
• Finally replace the arguments to the fillRect() method to 50,50,200,200.
• Next go to the method action. After the line mymap.iterate() add the line addPoint();. This adds a new point after each iteration to the list of points to be plotted.
• Finally we have to define the contents of this new method addPoint(). After the closing curly brace of the paint() method add the following code

  
  private void addPoint(){
  double xscale=10.0;
  double yscale=200.0;
  int xoffset=50;
  int yoffset=250;
  int ix,iy;
  ix=xoffset+(int)(xscale*counter);
  iy=yoffset-(int)(yscale*mymap.getX());
  x[counter]=ix;
  y[counter]=iy;
  counter++;
  if (counter==21) counter=0;
  }
  

  How does this work ? First, the pair of numbers (x,n) (the value of x and the number of iterations) must be converted to pixel values on the computer screen (i.e integers which run from 1 through 300 - the size of the applet). This is what is accomplished by the first 2 lines. Notice that we have defined x and y offsets on the screen and x and y scaling factors which do the conversion to screen coordinates. Then these new pixel coordinates are added to the arrays x[],y[]. Finally the repaint(); command calls the paint() method and causes the points to be plotted to the screen. The final if statement just makes sure that you can only plot up to 21 iterations after which it starts again.
• Make all these changes, recompile the code (javac *.java), change the file permissions (chmod 644 *.class and chmod 644 Simple2.html) and load the applet (point Netscape at web.syr.edu/yourSUnixuserid/PHY307/Simple2/Simple2.html). Does it work ?

Drawing the Sierpinski gasket

1. Go to the Labs section of the PHY307 pages. Load the applet Sierpinski Applet. Hit the button. You should see the Sierpinski triangle we discussed in class appear slowly on the screen. The applet is iterating a 2d map similar to the logistic map and producing a set of (x,y) values which are then plotted to the screen. The Sierpinski triangle corresponds to a very special choice of 2D mapping function.

1. Email me the url to your Web page so that I can take a look at your working Simple2 applet.