Science and Computers -- PHY307/607

Improving your HelloWorldApplet

• First login to your SUnix account as before (login, and double click the Secure Telnet icon which should present you with a login prompt to a SUnix machine).
• Go to your directory public_html/PHY307 by typing the command cd public_html/PHY307. Type the command cp Hwa1.java Hwa2.java to create a copy named Hwa2.java of your original file Hwa1.java.
• To start up an editing session of this new file type pico Hwa2.java. Go to the line before the line g.setFont(). Add the two lines

  
  g.setColor(Color.yellow);
  g.fillRect(50,50,xsize-100,ysize-100);
  
  

• Change the name of the class from Hwa1 to Hwa2 (i.e find the line class Hwa1 ... and change it to class Hwa2) This should be the second line of the file.
• Save the file by hitting ctrl-O and then return.
• Recompile the code by executing the command javac Hwa2.java at the SUnix prompt.
• Change the file permissions as before by typing chmod 644 Hwa2.class.
• We need to lauch this new version of the applet from an html page. So first copy the file Hwa1.html to a new file Hwa2.html by typing the UNIX command cp Hwa1.html Hwa2.html.
• Now use pico to edit this new file Hwa2.html so that the Java applet that is loaded is not Hwa1.class as before but the new file Hwa2.class (i.e you will have to modify the code=... parameter of the applet tag)
• Also, if you have not already done so add parameters to the applet tag to specify the applet size. Thus the line should now look like:

  < applet code=Hwa2.class width=300 height=200 > < /applet >
  

• Change the file permissions on this file by typing chmod 644 Hwa2.html
• Fire up Netscape and point it at your homepage.(i.eweb.syr.edu/~yourSUnixusername/PHY307/Hwa2.html
  IMPORTANT- Sometimes Netscape caches copies of Web pages and Java applets on disk so that hitting reload by itself does not always get the most recent version of the applet off the network. If this happens at any time try holding down the shift key at the same time as hitting reload - this forces a reloading of Java code for sure.

1. What do you see ?
2. What do you think the routine (Java calls them methods) setColor() does ?
3. What do you think the method fillRect() does ?
4. Edit Hwa2.java so that the background color is now red and the writing is now yellow. Recompile and check your changes work ...

Running a real Java applet - a simple chaos experiment

1. In Netscape go to the PHY307 homepage. Look under the LABS section and link to the Java applet MappingApplet. You should see a graph appear within your Web page.
2. The graph shows successive iterates of the logistic map we discussed in class. That is a new value for x is gotten from the equation

   
   x_(n+1)=ax_n(1-x_n)
   
   

   A new iteration is done by clicking on the Iterate button. The value of the iterate x is shown by the y coordinate while the number of iterations is shown by the x coordinate. The x scale runs to 10 -- where is iterate 11 plotted ? The x-axis always shows (up to) the last 10 iterations.
3. Type the value 0.8 into the a= box. Hit return now (this is very important - otherwise the change to a will not be registered). Also type a value of 0.1 into the x= box and also hit return. What is the value of x after many iterations ? Sketch a graph of what you see.
4. Keeping the same value of a change the initial value of x to 0.05. What is final value of x after many iterations. What is the final value when the initial value of x is set as 0.2 ?
5. Now change a to 1.5 and set x back to 0.1. Again sketch a graph of how x changes under repeated iteration. Does the final value of x depend on its initial value ?
6. What happens to the iteration for a=2.5 ? All of the experiments so far have shown that after large numbers of iterations the values of x approach a constant (which depends on a) independent of the initial value of x. This is called fixed point behavior.
7. Now set a=3.2 and x=0.5. Iterate again. What do you see ? Sketch the iterate graph after many iterations. Write down the values of x you see after many iterations (you can read them off the x= box). This is called periodic behavior.
8. What happens if you set a=3.53 ? Sketch the iterate graph after many iterations. What are the values of x that you see ?
9. Do a similar experiment at a=3.55 and now comment on the shape of the graph and the values of x that are seen.
10. Finally set a=3.8 and iterate. Comment - you are now in a chaotic regime !