Brewing Java: A Tutorial

Table of Contents

• Part 1: Why Java's Cool
  • Installing Java
    • Windows Installation Instructions
    • Unix Installation Instructions
  • Running Your First Applet
    • Applets in Netscape
• Part 2:The Syntax
  • Hello World: The Application
    • Examining Hello World
    • Braces and Blocks
    • Comments
    • Data and Variables
    • Command Line Arguments
    • If
    • Else
    • Variables and Arithmetic Expressions
  • Classes and Objects: A First Look
    • Interfaces
  • FahrToCelsius
    • Floating Point Variables
  • The For Statement
  • Assignment, Increment and Decrement Operators
  • Methods
    • Recursive Methods
  • Arrays
    • Creating Arrays
    • Counting Digits
    • Two Dimensional Arrays
    • Multidimensional Arrays
    • Unbalanced Arrays
    • Searching
    • Sorting
  • Catching Exceptions
  • File I/O and Streams
    • Interactively communicating with the user
    • Reading Numbers
    • Reading Formatted Data
    • Writing a text file
    • Reading a text file
  • Summing Up
• Part 3: Applets
  • Hello World: The Applet
    • Examining the Hello World Applet
  • The APPLET HTML Tag
    • Passing Parameters to Applets
  • Events and Applets
    • Event Tutor Applet
    • Making a List
    • The Events
  • Drawing Text
  • Drawing Graphics: Lines, Circles, Rectangles and Colors
    • Drawing Rectangles
    • Drawing Lines
  • Taking Action: Threads
    • Bozo Sort
  • Interaction: Mouse and Keyboard Input
    • Mouse Input: Java Doodle
    • Keyboard Input: TypeWriter
• Part 4: Objects, Classes, Methods, and Interfaces
  • What is Object Oriented Programming?
    • The History of Programming
    • Classes and Objects
    • Methods
    • Some Advocacy
  • A Non-Trivial Examples: Complex Numbers
    • toString Methods
    • Polymorphism
  • Scope: Calling the Complex Class From External Classes
  • The Mandelbrot Set
• Acknowledgements

Part 1: Why Java's Cool

People are excited about Java because of what it lets them do. Java was the first way to include inline sound and animation in a web page. Java also lets users interact with a web page. Instead of just reading it and perhaps filling out a form, users can now play games, calculate spreadsheets, chat in realtime, get continuously updated data and much, much more.

Here are just a few of the many things Java can do for a web page:

• Inline sounds that play in realtime whenever a user loads a page
• Music that plays in the background on a page
• Cartoon style animations
• Realtime video
• Multiplayer interactive games

Java is a programming language for distributed applications. It doesn't just allow you to add new types of content to your pages like Netscape and Internet Explorer do. Rather it lets you add both the content and the code necessary to interact with that content. You no longer need to wait for the next release of a browser that supports your preferred image format or special game protocol. With Java you send browsers both the content and the program necessary to view this content at the same time!

Let's think about what this means for a minute. Previously you had to wait for all the companies that make the web browsers your readers use to update their browsers before you could use a new content type. Then you had to hope that all your readers actually did update their browsers. Java compatibility is a feature that any browser can implement and by so doing implement every feature!

For instance let's say you want to use EPS files on your Web site. Previously you had to wait until at least one web browser implemented EPS support. Now you don't wait. Instead you can write your own code to view EPS files and send it to any client that requests your page at the same time they request the EPS file.

Or suppose you want people to be able to search your electronic card catalog. However the card catalog database exists on a mainframe system that doesn't speak HTTP. Before Java you could hope that some browser implemented your proprietary card catalog protocol; (fat chance) or you could try to program some intermediate cgi-bin on a UNIX box that can speak HTTP and talk to the card catalog, not an easy task. With Java when a client wants to talk to your card catalog you can send them the code they need to do so. You don't have to try to force things through an httpd server on port 80 that were never meant to go through it.

If that were all Java was, it would still be more interesting than a <marquee> or <frame> tag in some new browser beta. But there's a lot more. Java is platform independent. A Java program can run equally well on any architecture that has a Java enabled browser. With the release of Netscape Navigator 2.0 that includes Windows 95, Windows NT, the MacOS, Sun Solaris, Sun OS 4.1.3, SGI IRIX, OSF/1, HP-UX with more to come. But wait. There's more!

Java isn't just for web sites. Java is a programming language that lets you do almost anything you can do with a traditional programming langauge like Fortran or C++. However Java has learned from the mistakes of its predecessors. It is considerably cleaner and easier to use than those languages.

As a language Java is

Simple

Java has the bare bones functionality needed to implement its rich feature set. It does not add lots of syntactic sugar or unnecessary features.

Object-Oriented

Almost everything in Java is either a class, a method or an object. Only the most basic primitive operations and data types (int, for, while, etc.) are at a sub-object level.

Platform Independent

Java programs are compiled to a byte code format that can be read and run by interpreters on many platforms including Windows 95, Windows NT, and Solaris 2.3 and later.

Safe

Java code can be executed in an environment that prohibits it from introducing viruses, deleting or modifying files, or otherwise performing data destroying and computer crashing operations.

High Performance

Java can be compiled on the fly with a Just-In-Time compiler (JIT) to code that rivals C++ in speed.

Multi-Threaded

Java is inherently multi-threaded. A single Java program can have many different things processing independently and continuously.

Installing Java

Natural Intelligence has its own Java environment for the Mac called Roaster. Borland is also working a Java development environment to be released in the first half of 1996. Various third-party efforts are under way to port Java to other platforms including the Amiga, Windows 3.1, OS/2 and others.

The basic Java environment consists of a web browser that can play Java applets, a Java compiler to turn to Java source code into byte code, and a Java interpreter to run Java programs. These are the three key components of a Java environment. You'll also need a text editor like Brief or BBEdit. Other tools like a debugger, a visual development environment, documentation and a class browser are also nice but aren't absolutely necessary.

Note that it isn't necessary to get all three of these from the same source. For instance Netscape is committed to providing a Java-enabled web browser. However it will only provide a Java compiler with the next version of its server products.

Sun has made the Java Developers Kit available for its supported platforms. It includes an applet viewer that will let you view and test your applets. The JDK also includes the javac compiler, the java interpreter, the javaprof profiler, the javah header file generator (for integrating C into your Java code), the Java debugger and limited documentation. However most of the documentation for the API and the class library is on Sun's web site.

You can ftp the programs from the following sites:

• USA
  • ftp://ftp.javasoft.com/pub/
  • ftp://www.blackdown.org/pub/Java/pub/
  • ftp://ftp.science.wayne.edu/pub/java/
  • ftp://metalab.unc.edu/pub/languages/
  • ftp://java.dnx.com/pub/
• Germany: ftp://sunsite.informatik.rwth-aachen.de/pub/mirror/java.sun.com/JDK-beta-win32-x86.exe
• Korea: ftp://ftp.kaist.ac.kr/pub/java/e
• China: ftp://math01.math.ac.cn/pub/sunsite
• Japan: ftp://ftp.glocom.ac.jp/mirror/java.sun.com/
• Sweden: ftp://ftp.luth.se/pub/infosystems/www/hotjava/pub/
• Singapore: ftp://ftp.iss.nus.sg/pub/java/
• United Kingdom: ftp://sunsite.doc.ic.ac.uk/packages/java/

Macintosh Installation Instructions

It may be helpful to make aliases of the Applet Viewer, the Java Compiler and the Java Runner and put them on your desktop for ease of dragging and dropping later, especially if you have a large monitor.

Windows Installation Instructions

You will need to add C:\java\bin directory to your PATH environment variable

In addition to the java files, the archive includes two common DLL's:

• MSVCRT20.DLL
• MFC30.DLL

Unix Installation Instructions

The Unix release is a compressed tar file. You will need about nine megabytes of disk space to uncompress and untar the JDK. Double that would be very helpful. You do this with the commands:

% uncompress JDK-1_0_2-solaris2-sparc.tar.Z
% tar xvf JDK-1_0_2-solaris2-sparc.tar

You now need to add /usr/local/java/bin directory to your PATH environment variable. You use one of the following commands depending on your shell.

csh, tcsh: 
	% set path=($PATH /usr/local/java/bin)
sh: 
	% PATH=($PATH /usr/local/java/bin); export $PATH

Running Your First Applet

Unix Instructions

1. Open a command line prompt, and cd to one of the directories in /usr/local/java/demo, for example

   % cd /usr/local/java/demo/TicTacToe 
   

2. Run the appletviewer on the html file:

   % appletviewer example1.html 

3. Play Tic-Tac-Toe! The algorithm was deliberately broken so it is possible to win.

Macintosh Instructions

1. Start the Applet Viewer by double-clicking it.
2. Select Open... from the File menu and navigate into the java folder, then the Sample Applets folder, then the TicTacToe folder.
3. Select the file example1.html and click on the Open button. Alternately you can drag and drop this file onto the Applet Viewer.
4. Play Tic-Tac-Toe! The algorithm was deliberately broken so it is possible to win.

Windows Instructions

1. Open a DOS window, and cd to one of the directories in C:\JAVA\DEMO, for example

   C:< cd C:\JAVA\DEMO\TicTacToe 
   

2. Run the appletviewer on the html file:

   C:< appletviewer example1.htm 

3. Play Tic-Tac-Toe! The algorithm was deliberately broken so it is possible to win.

Hot Tip: Getting Rid of that Annoying License Dialog Box

Applets in Netscape

Part 2:The Syntax

Hello World: The Application

The following is the Hello World Application as written in Java. Type it into a text file or copy it out of your web browser, and save it as a file named HelloWorld.java.

class HelloWorld {

  public static void main (String args[]) {

    System.out.println("Hello World!");

  }
  
}

1. Did you put a semicolon after System.out.println("Hello World")?
2. Did you include the closing bracket?
3. Did you type everything exactly as it appears here? In particular did you use the same capitalization? Java is case sensitive. class is not the same as Class for example.
4. Were you in the same directory as HelloWorld.java when you typed javac HelloWorld.java?

Once your program has compiled successfully, the compiler places the executable output in a file called HelloWorld.class in the same directory as the source code file. You can then run the program by typing java HelloWorld at the command prompt. As you probably guessed the program responds by printing Hello World! on your screen.

Congratulations! You've just written your first Java program!

Examining Hello World

For now the initial class statement may be thought of as defining the program name, in this case HelloWorld. The compiler actually got the name for the class file from the class HelloWorld statement in the source code, not from the name of the source code file. If there is more than one class in a file, then the Java compiler will store each one in a separate .class file. For reasons we'll see later it's advisable to give the source code file the same name as the main class in the file plus the .java extension.

The initial class statement is actually quite a bit more than that since this "program" can be called not just from the command line but also by other parts of the same or different programs. We'll see more in the section on classes and methods below.

The HelloWorld class contains one method, the main method. As in C the main method is where an application begins executing. The method is declared public meaning that the method can be called from anywhere. It is declared static meaning that all instances of this class share this one method. (If that last sentence was about as intelligible as Linear B, don't worry. We'll come back to it later.) It is declared void which means, as in C, that this method does not return a value. Finally we pass any command line arguments to the method in an array of Strings called args. In this simple program there aren't any command line arguments though.

Finally when the main method is called it does exactly one thing: print "Hello World" to the standard output, generally a terminal monitor or console window of some sort. This is accomplished by the System.out.println method. To be more precise this is accomplished by calling the println() method of the static out field belonging to the System class; but for now we'll just treat this as one method.

One final note: unlike the printf function in C the System.out.println method does append a newline at the end of its output. There's no need to include a \n at the end of each string to break a line.

Exercises

1. What happens if you change the name of the source code file, e.g. HelloEarth.java instead of HelloWorld.java?
2. What happens if you keep the name of the source code file the same (HelloWorld.java) but change the class's name, e.g. class HelloEarth?

Braces and Blocks

Blocks are important both syntactically and logically. Without the braces the code wouldn't compile. The compiler would have trouble figuring out where one method or class ended and the next one began. Similarly it would be very difficult for someone else reading your code to understand what was going on. For that matter it would be very difficult for you, yourself to understand what was going on. The braces are used to group related statements together. In the broadest sense everything between matching braces is executed as one statement (though depending not necessarily everything inside the braces is executed every time).

Blocks can be hierarchical. One block can contain one or more subsidiary blocks. In this case we have one outer block that defines the HelloWorld class. Within the HelloWorld block we have a method block called "main".

In this tutorial we help to identify different blocks with indentation. Every time we enter a new block we indent our source code by two spaces. When we leave a block we deindent by two spaces. This is a common convention in many programming languages. However it is not part of the language. The code would produce identical output if we didn't indent it. In fact I'm sure you'll find a few examples here where I haven't followed convention precisely. Indentation makes the code easier to read and understand, but it does not change its meaning.

Comments

// This is the Hello World program in Java
class HelloWorld {

    public static void main (String args[]) {
      /* Now let's print the line Hello World */
      System.out.println("Hello World");
      
  }

}

Data and Variables

// This is the Hello Rusty program in Java
class HelloRusty {

    public static void main (String args[]) {
    
      // You may feel free to replace "Rusty" with your own name
      String name = "Rusty";
      
      /* Now let's say hello */
      System.out.print("Hello ");
      System.out.println(name);
  }

}

Command Line Arguments

What we need is a way to change the name at runtime rather than at compile time. (Runtime is when we type java HelloRusty. Compile time is when we type javac HelloRusty.java). To do this we'll make use of command-line arguments. They allow us to type something like Java Hello Gloria and have the program respond with "Hello Gloria". Here's the code:

// This is the Hello program in Java
class Hello {

    public static void main (String args[]) {
    
      /* Now let's say hello */
      System.out.print("Hello ");
      System.out.println(args[0]);
  }

}

This isn't very hard is it? In fact we've even gotten rid of the name variable from the HelloRusty program. We're using args[0] instead. args is what is known as an array. An array stores a series of values. The values can be Strings as in this example, numbers, objects or any other kind of Java data type.

args is a special array that holds the command line arguments. args[0] holds the first command line argument. args[1] holds the second command line argument, args[2] holds the third command line argument and so on.

At this point almost everyone reading this is probably saying "Whoa, that can't be right." However why you're saying depends on your background.

If you've never programmed before or if you've programmed only in Pascal or Fortran, you're probably wondering why the first element of the array is at position 0, the second at position 1, the third at position 2 instead of the clearly more sensible element 1 being the first element in the array, element 2 being the second and so on. All I can tell you is that this is a holdover from C where this convention almost made sense.

On the other hand if you're used to C you're probably upset because args[0] is the first command line argument instead of the command name. The problem is that in Java it's not always clear what the command name is. For instance in the above example is it java or Hello? On some systems where Java runs there may not even be a command line, the Mac for example.

Now you should experiment with this program a little. What happens if instead of typing java Hello Gloria you type java Hello Gloria and Beth? What if you leave out the name entirely, i.e. java Hello?

That was interesting wasn't it? You should have seen something very close to

Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException at Hello.main(C:\javahtml\Hello.java:7)

What happened was that since we didn't give Hello any command line arguments there wasn't anything in args[0]. Therefore Java kicked back this not too friendly error message about an "ArrayIndexOutOfBoundsException." That's a mouthful. We'll see one way to fix it in the next section.

If

All programming languages have some form of an if statement that allows you to test conditions. In the previous code we should have tested whether there actually were command line arguments before we tried to use them.

All arrays have lengths and we can access that length by referencing the variable arrayname.length. (Experienced Java programmers will note that this means that the array is an object which contains a public member variable called length.) We test the length of the args array as follows:

// This is the Hello program in Java
class Hello {

    public static void main (String args[]) {
    
      /* Now let's say hello */
      System.out.print("Hello ");
      if (args.length > 0) {
        System.out.println(args[0]);
      }
  }

}

What we did was wrap the System.out.println(args[0]) statement in a conditional test, if (args.length > 0) { }. The code inside the braces, System.out.println(args[0]), now gets executed if and only if the length of the args array is greater than zero. In Java numerical greater than and lesser than tests are done with the > and < characters respectively. We can test for a number being less than or equal to and greater than or equal to with <= and >= respectively.

Testing for equality is a little trickier. We would expect to test if two numbers were equal by using the = sign. However we've already used the = sign to set the value of a variable. Therefore we need a new symbol to test for equality. Java borrows C's double equals sign, ==, to test for equality.

It's not uncommon for even experienced programmers to write == when they mean = or vice versa. In fact this is a very common cause of errors in C programs. Fortunately in Java, you are not allowed to use == and = in the same places. Therefore the compiler can catch your mistake and make you fix it before you run the program.

All conditional statements in Java require boolean values, and that's what the ==, <, >, <=, and >= operators all return. A boolean is a value that is either true or false. Unlike in C booleans are not the same as ints, and ints and booleans cannot be cast back and forth. If you need to set a boolean variable in a Java program, you have to use the constants true and false. false is not 0 and true is not non-zero as in C. Boolean values are no more integers than are strings.

Experienced programmers may note that there was an alternative method to deal with the ArrayIndexOutOFBoundsException involving try and catch statements. We'll return to that soon.

Else

The cosmetic bug here was that if we didn't include any command line arguments, although the program didn't crash, it still didn't say Hello. The problem was that we only used System.out.print and not System.out.println. There was never any end of line character. It was like we typed in what we wanted to say, but never hit the return key.

We could fix this by putting a System.out.println(""); line at the end of the main method, but then we'd have one too many end-of-lines if the user did type in a name. We could add an additional if statement like so:

// This is the Hello program in Java
class Hello {

    public static void main (String args[]) {
    
      /* Now let's say hello */
      System.out.print("Hello ");
      if (args.length > 0) {
        System.out.println(args[0]);
      }
      if (args.length <= 0) {
        System.out.println("whoever you are");
      }
  }

}

// This is the Hello program in Java
class Hello {

    public static void main (String args[]) {
    
      /* Now let's say hello */
      System.out.print("Hello ");
      if (args.length > 0) {
        System.out.println(args[0]);
      }
      else {
        System.out.println("whoever you are");
      }
  }

}

We're not just limited to two cases though. We can combine an else and an if to make an else if and use this to test a whole range of mutually exclusive possibilities. For instance here's a version of the Hello program that handles up to four names on the command line:

// This is the Hello program in Java
class Hello {

    public static void main (String args[]) {
    
      /* Now let's say hello */
      System.out.print("Hello ");
      if (args.length == 0) {
        System.out.print("whoever you are");
      }
      else if (args.length == 1) {
        System.out.println(args[0]);
      }
      else if (args.length == 2) {
        System.out.print(args[0]);
        System.out.print(" ");
        System.out.print(args[1]);
      }      
      else if (args.length == 3) {
        System.out.print(args[0]);
        System.out.print(" ");
        System.out.print(args[1]);
        System.out.print(" ");
        System.out.print(args[2]);
      }      
      else if (args.length == 4) {
        System.out.print(args[0]);
        System.out.print(" ");
        System.out.print(args[1]);
        System.out.print(" ");
        System.out.print(args[2]);
        System.out.print(" ");
        System.out.print(args[3]);
      }      
      else {
        System.out.print(args[0]);
        System.out.print(" ");
        System.out.print(args[1]);
        System.out.print(" ");
        System.out.print(args[2]);
        System.out.print(" ");
        System.out.print(args[3]);
        System.out.print(" and all the rest!");
       }
      System.out.println();
  }

}

else {
  System.out.print(args[0] + " " + args[1] + " " + args[2] + " " + args[3] + " and all the rest!");
}

Exercises

1. Rework the entire program to use no more than one print method in each block.

2. A truly elegant solution to this problem relies on statements that haven't been introduced yet, notably for. However there is a more elegant and space efficient solution that accomplishes everything we did above, does not use the + operator, and uses only if's and a single else. No else if's are needed. Can you find it?

Variables and Arithmetic Expressions

while there's more data {
  Read a Line of Data
  Do Something with the Data
}

There are many different kinds of loops in Java including while, for, and do while loops. They differ primarily in the stopping conditions used.

For loops typically iterate a fixed number of times and then exit. While loops iterate continuously until a particular condition is met. You usually do not know in advance how many times a while loop will loop.

In this case we want to write a loop that will print each of the command line arguments in succession, starting with the first one. We don't know in advance how many arguments there will be, but we can easily find this out before the loop starts using the args.length. Therefore we will write this with a for loop. Here's the code:

// This is the Hello program in Java
class Hello {

    public static void main (String args[]) {
    
      int i;
    
      /* Now let's say hello */
      System.out.print("Hello ");
      for (i=0; i < args.length; i = i+1) {
        System.out.print(args[i]);
        System.out.print(" ");
      }
      System.out.println();
  }

}

Then we begin the program by saying "Hello" just like before.

Next comes the for loop. The loop begins by initializing the counter variable i to be zero. This happens exactly once at the beginning of the loop. Programming tradition that dates back to Fortran insists that loop indices be named i, j, k, l, m and n in that order. This is purely a convention and not a feature of the Java language. However anyone who reads your code will expect you to follow this convention. If you choose to violate the convention, try to give your loop variables mnemonic names like counter or loop_index.

Next is the test condition. In this case we test that i is less than the number of arguments. When i becomes equal to the number of arguments, (args.length) we exit the loop and go to the first statement after the loop's closing brace. You might think that we should test for i being less than or equal to the number of arguments; but remember that we began counting at zero, not one.

Finally we have the increment step, i=i+1. This is executed at the end of each iteration of the loop. Without this we'd continue to loop forever since i would always be less than args.length. (unless, of course, args.length were less than or equal to zero. When would this happen?).

Sidebar: Why Algebra teachers hate Basic and aren't that fond of C

The notable exceptions are Pascal (and the Pascal derivatives Modula-2, Modula-3 and Oberon), Ada, and Eiffel where = does in fact mean equality and where := is the assignment operator. Math teachers are very fond of their equal sign and don't like to see it abused. This is one reason why Pascal is still the most popular language for teaching programming, especially in schools where the Computer Science department is composed mainly of math professors.

Needless to say math professors hate languages like Basic where, depending on context, = can mean either assignment or equality.

Exercises

1. What happens now if we don't give the Hello program any command line arguments? We aren't testing the number of command line arguments anymore so why isn't an ArrayIndexOutOfBoundsException thrown?

2. For math whizzes only: I lied. In certain interpretations of certain number systems the statement i = i + 1 does have a valid solution for i. What is it?

Classes and Objects: A First Look

All the action in Java programs takes place inside class blocks, in this case the HelloWorld class. In Java almost everything of interest is either a class itself or belongs to a class. Methods are defined inside the classes they belong to. This may be a little confusing to C++ programmers who are used to defining all but the simplest methods outside the class block, but this approach is really more sensible. C++ takes the road it does primarily out of desire to be compatible with C, not out of good object-oriented design. Both syntactically and logically everything in Java happens inside a class.

Even basic data primitives like integers often need to be incorporated into classes before you can do many useful things with them. The class is the fundamental unit of Java programs, not source code files like in C. For instance consider the following Java program:

class HelloWorld {

  public static void main (String args[]) {

    System.out.println("Hello World");

  }

}

class GoodbyeWorld {

  public static void main (String args[]) {

    System.out.println("Goodbye Cruel World!");

  }

}

The second class is a completely independent program. Type java GoodbyeWorld and then type java HelloWorld. These programs run and execute independently of each other although they exist in the same source code file. Off the top of my head I can't think of why you might want two separate programs in the same file, but if you do the capability is there.

It's more likely that you'll want more than one class in the same file. In fact you'll see source code files with many classes and methods.

In fact there are a few statements that can, at least at first glance, appear outside a class. Import statements appear at the start of a file outside of any classes. However the compiler replaces them with the contents of the imported file which consists of, you guessed it, more classes.

Interfaces

FahrToCelsius

// Print a Fahrenheit to Celsius table

class FahrToCelsius  {

  public static void main (String args[]) {
  
  int fahr, celsius;
  int lower, upper, step;

  lower = 0;      // lower limit of temperature table
  upper = 300;  // upper limit of temperature table
  step  = 20;     // step size

  fahr = lower;
  while (fahr <= upper) {  // while loop begins here
    celsius = 5 * (fahr-32) / 9;
    System.out.print(fahr);
    System.out.print(" ");
    System.out.println(celsius);
    fahr = fahr + step;
  } // while loop ends here
} // main ends here

} //FahrToCelsius ends here 

Then we initialize the variables using statements like "lower = 0". This sets lower's initial value to 0. When used this way the equals sign is called the assignment operator.

After establishing the initial values for all our variables we go into the loop which does the main work of our program. At the beginning of each iteration of the loop (fahr <= upper) checks to see if the value of fahr is in fact less than or equal to the current value of upper. If it is then the computer executes the statements in the loop block (everything between "while loop begins here" and "while loop ends here".) Loops in Java are marked off by matching pairs of braces and may be nested.

celsius = 5 * (fahr-32) / 9; actually calculates the Celsius temperature given the fahrenheit temperature. The arithmetic operators here do exactly what you'd expect. * means multiplication. - is subtraction. / is division; and +, though not used in here, is addition. Precedence follows normal algebraic conventions, and can be rearranged through parentheses.

Java contains an almost complete set of arithmetic operators. Like C it is missing an exponentiation operator. For exponentiation you need to use the pow methods in the java.lang.Math package.

Printing output is very similar to what you've seen before. We use System.out.print(fahr) to print the fahrenheit value, then System.out.print(" ") to print a one-character string containing a space, and finally System.out.println(celsius); the Celsius value.

Finally we increment the value of fahr by step to move on to the next value in the table.

Floating Point Variables

Floating point numbers can represent a broader range of values than integers. For example you can write very large numbers like the speed of light (2.998E8 meters per second) and very small numbers like Plank's constant (6.63E-27 ) using the same number of digits. On the other hand you lose some precision that you probably didn't need for such large and small numbers anyway.

Some languages have a third kind of number called a fixed point number. This number has a set precision, for instance two decimal places, and is often useful in monetary calculations. Java has no fixed point data type.

Using floating point numbers is no harder than using integers. We can make our Fahrenheit to Celsius program more accurate merely by changing all our int variables into double variables.

// Print a more accurate Fahrenheit to Celsius table

class FahrToCelsius  {

  public static void main (String args[]) {

    double fahr, celsius;
    double lower, upper, step;

    lower = 0.0;      // lower limit of temperature table
    upper = 300.0;  // upper limit of temperature table
    step  = 20.0;     // step size
 
    fahr = lower;
    while (fahr <= upper) {  // while loop begins here
      celsius = 5.0 * (fahr-32.0) / 9.0;
      System.out.print(fahr);
      System.out.print(" ");
      System.out.println(celsius);
      fahr = fahr + step;
    } // while loop ends here
  } // main ends here

} //FahrToCelsius ends here 

What makes one type of number stronger than another? It's the ability to represent a broader spectrum of numbers. Since a byte can only represent 256 numbers it's weaker than a short which can stand for 65,535 different numbers including all the numbers a byte can represent. Similarly an int is stronger than a short. Floating point numbers are stronger than any integer type and doubles are the strongest type of all.

Therefore we could have left all the small constants as integers and the program output would have been unchanged. However it is customary to put in decimal points to remind yourself and anyone else who may be unlucky enough to have to read your code, exactly what is going on.

This applies to calculations that take place on the right hand side of an equal sign. The left hand side of the equals sign is a different story. In fact it's so different that programmers have given the different sides of the equals sign special names. The left-hand side is called an lvalue while the right hand side is called an rvalue.

An rvalue is a calculated result and as specified above it takes on the strongest type of any number involved in the calculation. On the other hand the lvalue has a type that must be defined before it is used. That's what all those float fahr, celsius; statements are doing. Once the type of an lvalue is defined it never changes. Thus if we declare fahr to be an int, then on the left hand side of an equals sign fahr will always be an int, never a float or a double or a long.

If you've been following along you may notice a problem here. What if the type on the left doesn't match the type on the right? e.g. what happens with code like the following?

class FloatToInt  {

  public static void main (String args[]) {

    int myInteger;

    myInteger = 9.7;

  } // main ends here

} //FloatToInt ends here 

class IntToFloat  {

  public static void main (String args[]) {

    float myFloat;
    int   myInteger;

    myInteger = 9;
    myFloat = myInteger;
    System.out.println(myFloat);

  } // main ends here

} //IntToFloat ends here 

Exercises

1. Have the FahrToCelsius program print a heading above the table.
2. Write a similar program to convert Celsius to Fahrenheit.

The For Statement

// Print a Fahrenheit to Celsius table

class FahrToCelsius  {

  public static void main (String args[]) {
  
    int fahr, celsius;
    int lower, upper, step;

    lower = 0;      // lower limit of temperature table
    upper = 300;  // upper limit of temperature table
    step  = 20;     // step size

    for (fahr=lower; fahr <= upper; fahr = fahr + step) {  
      celsius = 5 * (fahr-32) / 9;
      System.out.println(fahr + " " + celsius);
    } // for loop ends here

  } // main ends here

}

If that's unclear let's look at a simpler example:

//Count to ten

class CountToTen  {

  public static void main (String args[]) {
  
    int i;
    for (i=1; i <=10; i = i + 1) {  
      System.out.println(i);
    } 
    System.out.println("All done!");

}

}

For loops do not always work this smoothly. For instance consider the following program:

//Count to ten??

class BuggyCountToTen  {

  public static void main (String args[]) {
  
    int i;
    for (i=1; i <=10; i = i - 1) {  
      System.out.println(i);
    } 
    System.out.println("All done!");

}

}

Assignment, Increment and Decrement Operators

//Count to ten

class CountToTen  {

  public static void main (String args[]) {
    int i;
    for (i=1; i <=10; i++) {  
      System.out.println(i);
    } 
    System.out.println("All done!");

}

}

//Count to ten??

class BuggyCountToTen  {

  public static void main (String args[]) {
    int i;
    for (i=1; i <=10; i--) {  
      System.out.println(i);
    } 
    System.out.println("All done!");

  }

}

However what do you do when you want to increment not by one but by two? or three? or fifteen? We could of course write i = i + 15 but this happens frequently enough that there's another short hand for the general add and assign operation, +=. We would normally write this as i += 15. Thus if we wanted to count from 0 to 20 by two's we'd write:

class CountToTwentyByTwos  {

  public static void main (String args[]) {
    int i;
    for (i=0; i <=20; i += 2) {  
      System.out.println(i);
    } 
    System.out.println("All done!");

 } //main ends here

}

class CountToZeroByTwos  {

  public static void main (String args[]) {
    int i;
    for (i=20; i >= 0; i -= 2) {  
      System.out.println(i);
    } 
    System.out.println("All done!");

  }

}

There are also *= and /= operators that multiply and divide by their right hand sides before assigning. In practice you almost never see these because of the speed at which variables making use of them go to either zero or Inf. If you don't believe me consider the following cautionary tale.

Many centuries ago in India a very smart man is said to have invented the game of chess. This game greatly amused the king, and he became so enthralled with it that he offered to reward the inventor with anything he wished, up to half his kingdom and his daughter's hand in marriage.

Now the inventor of the game of chess was quite intelligent and not a little greedy. Not being satisfied with merely half the kingdom, he asked the king for the following gift:

"Mighty King," he said, "I am but a humble man and would not know what to do with half of your kingdom. Let us merely calculate my prize as follows. Put onto the first square of the chessboard a single grain of wheat. Then onto the second square of the chessboard two grains, and onto the third square of the chessboard twice two grains, and so on until we have covered the board with wheat."

Upon hearing this the king was greatly pleased for he felt he had gotten off rather cheaply. He rapidly agreed to the inventor's prize. He called for a bag of wheat to be brought to him, and when it arrived he began counting out wheat. However he soon used up the first bag and was not yet halfway across the board. He called for a second, and a third, and more and more, until finally he was forced to admit defeat and hand over his entire kingdom for lack of sufficient wheat with which to pay the inventor.

How much wheat did the king need? Let's try to calculate it. Although we won't use physical wheat, we will soon find ourselves in the same dire straits as the king. Remember that a chessboard has 64 squares.

class CountWheat  {

  public static void main (String args[]) {
  
    int i, j, k;

    j = 1;
    k = 0;

    for (i=1; i <= 64; i++) {
      k += j;
      System.out.println(k);
      j *= 2;
    } 
    System.out.println("All done!");

  }

}

class CountWheat {

  public static void main (String args[]) {
  
    long i, j, k;

    j = 1;
    k = 0;

    for (i=1; i <= 64; i++) {
      k += j;
      System.out.println(k);
      j *= 2;
    } 
    System.out.println("All done!");

  }

}

class CountWheat {

  public static void main (String args[]) {
  
  int i;
  double j, k;
  
  j = 1.0;
  k = 0.0;
  
  for (i=1; i <= 64; i++) {
      k += j;
      System.out.println(k);
      j *= 2;
  } 
  System.out.println("All done!");

}

}

Exercises

1. Would a float be big enough to count how many grains of wheat the king owes?

2. Why isn't there a ** or a // operator?

Methods

Each calculation part of a program is called a method. Methods are logically the same as C's functions, Pascal's procedures and functions, and Fortran's functions and subroutines.

The above programs have already used a number of methods although these were all methods provided by the system. When we wrote System.out.println("Hello World!"); in the first program we were using the System.out.println() method. (To be more precise we were using the println() method of the out member of the System class, but we'll talk more about that in Chapter 4.) The System.out.println() method actually requires quite a lot of code, but it is all stored for us in the System libraries. Thus rather than including that code every time we need to print, we just call the System.out.println() method.

You can write and call your own methods too. Let's look at a simple example. Java has no built-in factorial method so we'll write one. The following is a simple program that requests a number from the user and then calculates the factorial of that number.

We'll use two methods in the program, one that checks to see if the user has in fact entered a valid positive integer, and another that calculates the factorial. However we'll start by writing the main method of the program:

class Factorial {

  public static void main(String args[]) {

    int n;

    while ((n = getNextInteger()) >= 0)  {
      System.out.println(factorial(n));
    }

  } // main ends here

}

long factorial (long n) {

  int i;
  long result=1;
  
  for (i=1; i <= n; i++) {
   result *= i;
  }
  
  return result;

} // factorial ends here

class FactorialTest {

  public static void main(String args[]) {

    int n;
    int i;
    long result;

    for (i=1; i <=10; i++)  {
      result = factorial(i);
      System.out.println(result);
    }

  } // main ends here
  
  
  static long factorial (int n) {

  int i;
  long result=1;
  
  for (i=1; i <= n; i++) {
   result *= i;
  }
  
  return result;

} // factorial ends here


}

Let's take a closer look at the syntax of a method:

 static long factorial (int n) {

  int i;
  long result=1;
  
  for (i=1; i <= n; i++) {
   result *= i;
  }
  
  return result;

}

Next we decide whether the method is or is not static. Static methods have only one instance per class rather than one instance per object. All objects of the same class share a single copy of a static method. By default methods are not static.

Next we specify the return type. This is the value that will be sent back to the calling method when all calculations inside the method are finished. If the return type is int, for example, we can use the method anywhere we use a constant integer. If the return type is void then no value will be returned.

Next is the name of the method.

Then there are parentheses. Inside the parentheses we give names and types to the arguments of the method. A method may have no arguments or it may have one or several. These arguments can be used inside the method just like local variables.

Finally the rest of the method is enclosed in braces to make it a single block. The part inside braces is just like the main methods we've been exploring till now. There are variable declarations, some code, and finally something new, a return statement. The return statement sends a value back to the calling method. The type of this value must match the declared type of the method.

In general any line that looks like Text(arg1, arg2) or text(arg1) or text() is a method call. The compiler is responsible for distinguishing between parentheses that mean method calls and parentheses that serve as grouping operators in mathematical expressions like (3 + 7) * 2. The compiler does a very good job of this and you may safely assume that anything that isn't clearly an arithmetical expression is a method call.

Methods break up a program into logically separate algorithms and calculations. In still larger programs it's necessary to break up the data as well. The data can be separated into different classes and the methods attached to the classes they operate on. This is the heart of object oriented programming and the subject of Chapter 4 below.

Recursive Methods

You probably already see one problem with recursion. Where does it all end? In fact when you write recursive methods you have to be careful to include stopping conditions. Although Java doesn't put any particular limits on the depth to which you can expand a recursion, it is very possible to have a run-away recursion eat up all the memory in your computer.

Let's look at an example. n! (pronounced "En-factorial") is defined as n times n-1 times n-2 times n-3 ... times 2 times 1 where n is a positive integer. 0! is defined as 1. As you see n! = n time (n-1)!. This lends itself to recursive calculation, as in the following method:

public static long factorial (int n) {

  if (n == 0) {
    return 1;
  }
  else {
    return n*factorial(n-1);
  }

}

public static long factorial (int n) {

  if (n < 0) {
    return -1;
  } 
  else if (n == 0) {
    return 1;
  }
  else {
    return n*factorial(n-1);
  }

}

public static long factorial (int n) {

  long result = 1;
  
  for (int i = 1; i <= n; i++) {
    result *= i;
  }
  
  return result;

}

Here's an example of a recursive program for which I have not been able to find a simple, non-recursive equivalent method. The goal is to find all possible RAM configurations for a PC, given the size of the memory chips it will accept and the number of slots it has available. We are not concerned with how the RAM is arranged inside the PC, only with the total quantity of installed RAM. For some computers this can easily be calculated by hand. For instance Apple's PowerBook 5300 series comes with 8 megabytes of RAM soldered onto the logic board and one empty slot that can hold chips of 8, 16, 32 or 56 MB capacity. Therefore the possible Ram configurations are 8, 16, 24, 40 and 64 MB. However as the number of available slots and the number of available chip sizes increases this becomes a much more difficult problem. The following is a recursive program to calculate and print all possible RAM configurations:

import java.util.Hashtable;
import java.util.Enumeration;

public class RamConfig {

   static int[] sizes = {0, 8, 16, 32, 64};
   static Hashtable configs = new Hashtable(64);
   static int slots[] = new int[4];

   public static void main (String args[]) {

     System.out.println("Available DIMM sizes are: ");
     for (int i=0; i < sizes.length; i++) System.out.println(sizes[i]);

     fillSlots(slots.length - 1);
     System.out.println("Ram configs are: ");

     for (Enumeration e = configs.elements(); e.hasMoreElements(); ) {
       System.out.println(e.nextElement());    
     }
     
   }
   
  
  private static void fillSlots(int n) {
  
    int total;
     
    for (int i=0; i < sizes.length; i++) {
       slots[n] = sizes[i];
       if (n == 0) {
          total = 0;
          for (int j = 0; j < slots.length; j++) {
            total += slots[j];
          }
          configs.put(Integer.toString(total), new Integer(total));
       }
       else {
         fillSlots(n - 1);
       }
    }      
  
  }
  
}

Below is my variation of this benchmark. There are overloaded integer and floating point versions of the Tak method. Integer is used by default. If the -f flag is given on the command line, the floating point method is used. The number of passes to make may also be entered from the command line. If it is not, 1000 passes are made. The Java Date class is used to time that part of the test where the benchmarking is done.

import java.util.Date;


public class Tak {

  public static void main(String[] args) {
   
   boolean useFloat = false;
   int numpasses;
   
   for (int i = 0; i < args.length; i++) {
     if (args[i].startsWith("-f")) useFloat = true;
   }
   try {
     numpasses = Integer.parseInt(args[args.length-1]);
   }
   catch (Exception e) {
     numpasses = 1000;
   }
   
   Date d1, d2;
   if (useFloat) {
     d1 = new Date();
     for (int i = 0; i < numpasses; i++) {
        Tak(18.0f, 12.0f, 6.0f);
     }
     d2 = new Date();
   }
   else {
     d1 = new Date();
     for (int i = 0; i < numpasses; i++) {
        Tak(18, 12, 6);
     }
     d2 = new Date();
   
   }
   long TimeRequired = d2.getTime() - d1.getTime();
   double numseconds = TimeRequired/1000.0;
   
   System.out.println("Completed " + numpasses + " passes in " 
    + numseconds + " seconds" );
   System.out.println(numpasses/numseconds + " calls per second");
  
  }

  public static int Tak(int x, int y, int z) {
    if (y >= x) return z;
    else return Tak(Tak(x-1, y, z), Tak(y-1, z, x), Tak(z-1, x, y));   
  
  }

  public static float Tak(float x, float y, float z) {
    if (y >= x) return z;
    else return Tak(Tak(x-1.0f, y, z), Tak(y-1.0f, z, x), Tak(z-1.0f, x, y));   
  
  }

}

My Powerbook 5300 achieved speeds between 3.5 and 5 passes per second on this test. Sun's Mac VM was about 10% faster on this test than Natural Intelligence's. The heavily loaded Sparcstation at metalab.unc.edu (load average 4+) achieved a little more than 3 passes per second. Given the various external factors affecting machine performance, these are hardly scientific measurements. I'd be curious to hear what your results are.

Exercises

1. Find the non-recursive equivalent to the Ram Config algorithm.

Arrays

There are many ways to store lists of items including linked lists, sets, hashtables, binary trees and arrays. Which one you choose depends on the requirements of your application and the nature of your data. Java provides classes for many of these ways to store data and we'll explore them in detail in the chapter on the Java Class Library.

Arrays are probably the oldest and still the most generally effective means of storing groups of variables. An array is a group of variables that share the same name and are ordered sequentially from zero to one less than the number of variables in the array. The number of variables that can be stored in an array is called the array's dimension. Each variable in the array is called an element of the array.

An array can be visualized as a column of data like so:

I[0] I[1] I[2] I[3] I[4]

4 2 76 -90 6

In this case we're showing an integer array named I with five elements; i.e. the type of the array is int and the array has dimension 5.

Creating Arrays

Declaring Arrays

Like all other variables in Java an array must be declared. When you declare an array variable you suffix the type with [] to indicate that this variable is an array. Here are some examples:

int[] k;
float[] yt;
String[] names;

Allocating Arrays

k = new int[3];
yt = new float[7];
names = new String[50];

This is also our first look at the new operator. new is a reserved word in java that is used to allocate not just an array, but also all kinds of objects. Java arrays are full-fledged objects with all that implies. For now the main thing it implies is that we have to allocate them with new.

Initializing Arrays

You can use array elements wherever you'd use a similarly typed variable that wasn't part of an array.

Here's how we'd store values in the arrays we've been working with:

k[0] = 2;
k[1] = 5;
k[2] = -2;
yt[6] = 7.5f;
names[4] = "Fred";

For even medium sized arrays, it's unwieldy to specify each element individually. It is often helpful to use for loops to initialize the array. For instance here is a loop that fills an array with the squares of the numbers from 0 to 100.

float[] squares = new float[101];

for (int i=0; i <= 100; i++) {
  squares[i] = i*i;
}

• Watch the fenceposts! Since array subscripts begin at zero we need 101 elements if we want to include the square of 100.
• Although i is an int it becomes a float when it is stored in squares, since we've declared squares to be an array of floats.

float[] squares = new float[101];

for (int i=0, i < squares.length; i++) {
  squares[i] = i*i;
}

Shortcuts

We can declare and allocate an array at the same time like this:

int[] k = new int[3];
float[] yt = new float[7];
String[] names = new String[50];

int[] k = {1, 2, 3};
float[] yt = {0.0f, 1.2f, 3.4f, -9.87f, 65.4f, 0.0f, 567.9f};

Counting Digits

As our second example let's consider a class that counts the occurrences of the digits 0-9 in decimal expansion of the number pi, for example. This is an issue of some interest both to pure number theorists and to theologians. See, for example, Carl Sagan's Contact and John Updike's Roger's Version. More realistically we might wish to test the randomness of a random number generator. If a random number generator is truly random, all digits should occur with equal frequency over a sufficiently long period of time.

We will do this by creating an array of ten longs called ndigit. The zeroth element of ndigit will track the number of zeroes in the input stream; the first element of ndigit will track the numbers of 1's and so on. We'll test Java's random number generator and see if it produces apparently random numbers.

import java.util.*;

class RandomTest {

  public static void main (String args[]) {
  
    int[] ndigits = new int[10];
    double x;
    int n;
    
    Random myRandom = new Random();
  
    // Initialize the array 
    for (int i = 0; i < 10; i++) {
      ndigits[i] = 0;
    }

    // Test the random number generator a whole lot
    for (long i=0; i < 100000; i++) {
      // generate a new random number between 0 and 9
      x = myRandom.nextDouble() * 10.0;
      n = (int) x;
      //count the digits in the random number
      ndigits[n]++;
    }
    
    // Print the results
    for (int i = 0; i <= 9; i++) {
      System.out.println(i+": " + ndigits[i]);
    }
  }
  
}

Two Dimensional Arrays

	c0	c1	c2	c3
r0	0	1	2	3
r1	1	2	3	4
r2	2	3	4	5
r3	3	4	5	6
r4	4	5	6	7

Here we have an array with five rows and four columns. It has twenty total elements. However we say it has dimension four by five, not dimension twenty. This array is not the same as a five by four array like this one:

	c0	c1	c2	c3	c4
r0	0	1	2	3	4
r1	1	2	3	4	5
r2	2	3	4	5	6
r3	3	4	5	6	7

We need to use two numbers to identify a position in a two-dimensional array. These are the element's row and column positions. For instance if the above array is called J then J[0][0] is 0, J[0][1] is 1, J[0][2] is 2, J[0][3] is 3, J[1][0] is 1, and so on.

Here's how the elements in a four by five array called M are referred to:

M[0][0]	M[0][1]	M[0][2]	M[0][3]	M[0][4]
M[1][0]	M[1][1]	M[1][2]	M[1][3]	M[1][4]
M[2][0]	M[2][1]	M[2][2]	M[2][3]	M[2][4]
M[3][0]	M[3][1]	M[3][2]	M[3][3]	M[3][4]

Declaring, Allocating and Initializing Two Dimensional Arrays

The array examples above are filled with the sum of their row and column indices. Here's some code that would create and fill such an array:

class FillArray {

  public static void main (String args[]) {
  
    int[][] M;
    M = new int[4][5];
  
    for (int row=0; row < 4; row++) {
      for (int col=0; col < 5; col++) {
        M[row][col] = row+col;
      }
    }
    
  }
  
}

class IDMatrix {

  public static void main (String args[]) {
  
    double[][] ID;
    ID = new double[4][4];
  
    for (int row=0; row < 4; row++) {
      for (int col=0; col < 4; col++) {
        if (row != col) {
          ID[row][col]=0.0;
        }
        else {
          ID[row][col] = 1.0;
        }
      }
    }
    
  }
  
}

Exercises

1. Write a program to generate the HTML for the above tables.

Multidimensional Arrays

The syntax for three dimensional arrays is a direct extension of that for two-dimensional arrays. Here's a program that declares, allocates and initializes a three-dimensional array:

class Fill3DArray {

  public static void main (String args[]) {
  
    int[][][] M;
    M = new int[4][5][3];
  
    for (int row=0; row < 4; row++) {
      for (int col=0; col < 5; col++) {
        for (int ver=0; ver < 3; ver++) {
          M[row][col][ver] = row+col+ver;
        }
      }
    }
    
  }
  
}

The syntax for still higher dimensions is similar. Just add another pair pf brackets and another dimension.

Unbalanced Arrays

Searching

Unless you have some special knowledge of the contents of the array (for instance, that it is sorted) the quickest algorithm for searching an array is straight-forward linear search. Use a for loop to look at every element of the array until you find the element you want. Here's a simple method that prints the largest and smallest elements of an array:

   static void printLargestAndSmallestElements (int[] n) {
  
    int max = n[0];
    int min = n[0];
    
    for (int i=1; i < n.length; i++) {
      if (max < n[i]) {
        max = n[i];
      }
      if (min > n[i]) {
        min = n[i];
      }
    }
    
    System.out.println("Maximum: " + max);
    System.out.println("Minimum: " + min);
    
    return;
  
  }
  

Sorting

class Swap1 {

  public static void main(String args[]) {
  
   int a = 1;
   int b = 2;
   
   System.out.println("a = "+a);
   System.out.println("b = "+b);
   
   // swap a and b
   
   a = b;
   b = a;
   
   System.out.println("a = "+a);
   System.out.println("b = "+b);   
  
  }

}

a = 1
b = 2
a = 2
b = 2

class Swap2 {

  public static void main(String args[]) {
  
   int a = 1;
   int b = 2;
   int temp;
   
   System.out.println("a = "+a);
   System.out.println("b = "+b);
   
   // swap a and b
   
   temp = a;
   a = b;
   b = temp;
   
   System.out.println("a = "+a);
   System.out.println("b = "+b);   
  
  }

}

a = 1
b = 2
a = 2
b = 1

Bubble Sort

import java.util.*;

class BubbleSort {

  public static void main(String args[]) {
  
   int[] n;
   n = new int[10];
   Random myRand = new Random();
   
   // initialize the array
   for (int i = 0; i < 10; i++) {
     n[i] = myRand.nextInt();
   }
   
   // print the array's initial order
   System.out.println("Before sorting:"); 
   for (int i = 0; i < 10; i++) {
     System.out.println("n["+i+"] = " + n[i]);
   }
   
   boolean sorted = false;
   // sort the array
   while (!sorted) {
     sorted = true;
     for (int i=0; i < 9; i++) {
       if (n[i] > n[i+1]) {
         int temp = n[i];
         n[i] = n[i+1];
         n[i+1] = temp;
         sorted = false;
       }   
     }
   }

  // print the sorted array
  System.out.println();
  System.out.println("After sorting:");  
   for (int i = 0; i < 10; i++) {
     System.out.println("n["+i+"] = " + n[i]);
   }

  
  }

}

Catching Exceptions

// This is the Hello program in Java
class Hello {

    public static void main (String args[]) {
    
      /* Now let's say hello */
      System.out.print("Hello ");
      System.out.println(args[0]);
  }

}

Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException at Hello.main(C:\javahtml\Hello.java:7)

What happened was that since we didn't give Hello any command line arguments there wasn't anything in args[0]. Therefore Java kicked back this not too friendly error message about an "ArrayIndexOutOfBoundsException."

Previously we fixed this problem by testing the length of the array before we tried to access its first element. This worked well in this simple case, but this is far from the only such potential problem. If you were to check for every possible error condition in each line of code, you would find your code becoming bloated with more error checking than actual code. Moreover you then have to start checking for errors in the error conditions. In older languages like C, Basic and Fortran you sooner or later you find yourself resorting to goto or longjmp or other such ingredients in the recipe for illegible Spaghetti Code

The goal of exception handling is to be able to define the regular flow of the program in part of the code without worrying about all the special cases. Then, in a separate block of code, you cover the exceptional cases. This produces more legible code since you don't need to interrupt the flow of the algorithm to check and respond to every possible strange condition. The runtime environment is responsible for moving from the regular program flow to the exception handlers when an exceptional condition arises.

In practice what you do is write blocks of code that may generate exceptions inside try-catch blocks. You try the statements that generate the exceptions. Within your try block you are free to act as if nothing has or can go wrong. Then, within one or more catch blocks, you write the program logic that deals with all the special cases.

Here's an example of exception handling in Java using the Hello World program above:

// This is the Hello program in Java
class ExceptionalHello {

    public static void main (String args[]) {
    
      /* Now let's say hello */
      try {
        System.out.println("Hello " + args[0]);
      }
      catch (Exception e) {
        System.out.println("Hello whoever you are");      
      }
  }

}

Sometimes catching an exception can feel like a little yippy dog that finally catches a car. Now that it's got hold of the bumper between its teeth, what is it going to do with it? Many times there may not be much you can do. Bad exceptions stop the program by default. This is at least preferable to unhandled exceptions in most programming languages where the entire system can come crashing down around your feet with a core dump or worse. Sometimes you may want to this too. In that case you can call the System.exit(int) method to halt your running program.

Other times you may just break out of a loop you were in and continue with the rest of your code. This is most common when an exception isn't really unexpected or when it doesn't badly affect your program logic.

You may or may not print an error message. If you write an exception handler and you don't expect it to be called, then by all means put a

System.out.println("Error: " + e);

in your exception handler. That way if something does go wrong (and something always does) you'll at least know where it went wrong. However don't put an error message in exception handlers you expect to be exercised in the course of normal program flow. Remember, they're exceptions, not errors.

In the next section we'll see lots of examples of code that can possibly generate exceptions which must be caught. We'll talk more about exceptions in a later chapter, but this is the bare bones you need to know to respond to the exceptions generated by the java.io classes we'll be discussing in the next section.

File I/O and Streams

Streams are a big topic in Java and later we'll devote an entire chapter to them. For now we want to cover just the very basics that let you write files, read files and communicate with the user. In fact the System.out.println() statement we've been using all along is an implementation of Streams.

Interactively communicating with the user

import java.io.*;

class PersonalHello {

  public static void main (String args[])
    {
    
      byte name[] = new byte[100];
      int nr_read = 0;

      System.out.println("What is your name?");
      try {
        nr_read = System.in.read(name);
        System.out.print("Hello ");
        System.out.write(name,0,nr_read);
      }
      catch (IOException e) {
        System.out.print("I'm Sorry.  I didn't catch your name.");
      }
      
    }
    
}

Most of the reading and writing you do in Java will be done with bytes. (As you'll see later there are also ways to read text files directly into Strings.) Here we've started with an array of bytes that will hold the user's name.

First we print a query requesting the user's name. Then we read the user's name using the System.in.read() method. This method takes a byte array as an argument, and places whatever the user types in that byte array. Then, like before, we print "Hello." Finally we print the user's name.

The program doesn't actually see what the user types until he or she types a carriage return. This gives the user the chance to backspace over and delete any mistakes. Once the return key is pressed, everything in the line is placed in the array.

What happens if the user types more than 100 characters of text before hitting a carriage return? In many programming languages this would lead to a rather nasty program crash. It's also the sort of bug that often gets out the door in a shipping product since programmers often fail to test their programs against extreme inputs. However Java has been programmed a little more safely. System.in.read() won't read past the end of the array even though we didn't explicitly check to make sure the input was sufficiently small. My guess is that the System.in.read() method internally checks the length of the array it's been passed using the name.length property.

Reading Numbers

Next we promised to write a getNextInteger() method that will accept an integer from the user. Here it is:

  static int getNextInteger() {
  
    String line;
  
    DataInputStream in = new DataInputStream(System.in);
    try {
      line = in.readLine();
      int i = Integer.valueOf(line).intValue();
      return i;
    }
    catch (Exception e) {
      return -1;
    }
       
  } // getNextInteger ends here

Reading Formatted Data

Writing a text file

// Write the Fahrenheit to Celsius table in a file

import java.io.*;

class FahrToCelsius  {

  public static void main (String args[]) {

    double fahr, celsius;
    double lower, upper, step;

    lower = 0.0;    // lower limit of temperature table
    upper = 300.0;  // upper limit of temperature table
    step  = 20.0;   // step size

    fahr = lower;
  
    try {

      FileOutputStream fout =  new FileOutputStream("test.out");

      // now to the FileOutputStream into a PrintStream
      PrintStream myOutput = new PrintStream(fout);
  
      while (fahr <= upper) {  // while loop begins here
        celsius = 5.0 * (fahr-32.0) / 9.0;
        myOutput.println(fahr + " " + celsius);
        fahr = fahr + step;
      } // while loop ends here
  
    }  // try ends here
    catch (IOException e) {
      System.out.println("Error: " + e);
      System.exit(1);
    }
  
  } // main ends here

}

1. Open a FileOutputStream using a line like

   FileOutputStream fout =  new FileOutputStream("test.out");
   

   This line initializes the FileOutputStream with the name of the file you want to write into.

2. Convert the FileOutputStream into a PrintStream using a statement like

   PrintStream myOutput = new PrintStream(fout);
   

   The PrintStream is passed the FileOutputStream from step 1.

3. Instead of using System.out.println() use myOutput.println(). System.out and myOutput are just different instances of the PrintStream class. To print to a different PrintStream we keep the syntax the same but change the name of the PrintStream.

Reading a text file

// Imitate the Unix cat utility

import java.io.*;

class cat  {

  public static void main (String args[]) {
  
  String thisLine;

  //Loop across the arguments
  for (int i=0; i < args.length; i++) {
 
  //Open the file for reading
  try {
    FileInputStream fin =  new FileInputStream(args[i]);

    // now turn the FileInputStream into a DataInputStream
    try {
      DataInputStream myInput = new DataInputStream(fin);
  
      try {
        while ((thisLine = myInput.readLine()) != null) {  // while loop begins here
          System.out.println(thisLine);
        } // while loop ends here
      }
      catch (Exception e) {
       System.out.println("Error: " + e);
      }
    } // end try
    catch (Exception e) {
      System.out.println("Error: " + e);
    }
  
   } // end try
   catch (Exception e) {
    System.out.println("failed to open file " + args[i]);
    System.out.println("Error: " + e);
  }
  } // for end here
  
  } // main ends here

}

Summing Up

FahrToCelsius is a very basic application that could be written in almost any programming language from the most ancient machine code to the most advanced LISP machine. Nonetheless it is important to notice that Java solves this problem just as easily as would a language more commonly associated with numeric and scientific programming such as Fortran or C. In fact this code was translated almost verbatim from Kernighan and Ritchie. Only a few minor semantic changes were required to produce a valid, efficient Java program. Although Java has many, many features that make it suitable for complex object-oriented applications, it is also fully suitable for classic numerical programs, something that is not true of competitors like SmallTalk or LISP.

In fact Java can outperform even Fortran and C in numerical applications when precision, reliability and portability are more important than speed. Java's true arrays with bounds checking and its well-defined IEEE 754 floating point data types are especially useful in this regard.

Since there is as of yet no native architecture compiler for Java, it's too early to throw away your Fortran manuals. CPU intensive applications will still be coded in Fortran. The Java language itself (as opposed to its implementation) is also lacking in a couple of important respects for numeric computation. The lack of an exponentiation operator like Fortran's ** and the lack of a complex data type are both troublesome to longtime Fortran programmers. However neither is insurmountable.

Would anyone care to write a Fortran to Java translator?

In the next chapter we'll move beyond the 1970's to discuss more modern features of Java including Objects, Applets, Event Driven Programming and threads.

Part 3: Applets

In this chapter we're going to move into the 1980's. In particular we're going to work with event driven programming. This style of programming should be very familiar to Macintosh and Windows programmers. In those environments program logic doesn't flow from the top to the bottom of the program as it does in most procedural code. Rather the operating system collects events and the program responds to them. These events may be mouse clicks, keypresses, network data arriving on the Ethernet port, or any of about two dozen other possibilities. The operating system looks at each event, determines what program it was intended for, and places the event in the appropriate program's event queue.

Every application program has an event loop. This is just a while loop which loops continuously. On every pass through the loop the application retrieves the next event from its event queue and responds accordingly.

Java applets behave similarly. However the runtime environment (i.e. the browser) takes care of the event loop for the applet so there's no need to write one explicitly. Rather you need to have methods in your applet subclass that respond to each kind of event you want to process.

This is all fairly abstract until you see some concrete examples. Let's begin with a simple one.

Hello World: The Applet

import java.applet.Applet;    
import java.awt.Graphics; 
              
public class HelloWorldApplet extends Applet {

  public void paint(Graphics g) {
    g.drawString("Hello world!", 50, 25);
  }
  
}

First type in the source code and save it into file called HelloWorldApplet.java in the javahtml/classes directory. Compile this file by typing javac HelloWorldApplet.java at the command line prompt.

If all is well a file called HelloWorldApplet.class will be created. This file must be in your classes directory.

Now you need to create an HTML file that will include your applet. The following simple HTML file will do.

<HTML>
<HEAD>
<TITLE> Hello World </TITLE>
</HEAD>

<BODY>
This is the applet:<P>
<APPLET codebase="classes" code="HelloWorldApplet.class" width=200 height=200 ></APPLET>
</BODY>
</HTML>

This is the applet:
Hello World!

If the applet compiled without error and produced a HelloWorldApplet.class file, and yet you don't see the string "Hello World" in your browser chances are that the class file is in the wrong place. Make sure the .html file is in the javahtml directory and the compiled .class file is in the javahtml/classes directory.

Examining the Hello World Applet

import java.applet.Applet;    
import java.awt.Graphics;

The next change from the application is the Class definition:

public class HelloWorldApplet extends Applet

The extends keyword indicates that this class is a subclass of the Applet class; or, to put it another way, Applet is a superclass of HelloWorldApplet. The Applet class is defined in the java.applet.Applet package which we just imported. Since HelloWorldApplet is a subclass of the Applet class, our HelloWorldApplet automatically inherits all the functionality of the generic Applet class. Anything an Applet can do, the HelloWorldApplet can do too.

The next difference between the applet and the application is far less obvious (except maybe to a longtime C programmer). There's no main method! Applets don't need them. The main method is actually in the browser or the AppletViewer, not in the Applet itself. Applets are like plugin code modules for Adobe Photoshop that provide extra functionality, but can't run without a main program to host them.

Rather than starting at a specific place in the code applets are event driven. An applet waits for one of a series of events such as a key press, the mouse pointer being moved over the applets visible area, or a mouse click and then executes the appropriate event handler. Since this is our first program we only have one event handler, paint.

Most applets need to handle the paint event. This event occurs whenever a part of the applet's visible area is uncovered and needs to be drawn again.

The paint method is passed a Graphics object which we've chosen to call g. The Graphics class is defined in the java.awt.Graphics package which we've imported. Within the paint method we call g's drawString method to draw the string "Hello World!" at the coordinates (50,25). That's 50 pixels across and twenty-five pixels down from the upper left hand corner of the applet. We'll talk more about coordinate systems later. This drawing takes place whenever a portion of the screen containing our applet is covered and then uncovered and needs to be refreshed.

The APPLET HTML Tag

For reasons that remain a mystery to HTML authors everywhere, but possibly having something to do with packages and classpaths, if the applet resides somewhere other than the same directory as the page it lives on, then you don't just give a URL to its location. Rather you point at the directory where the .class file is using the CODEBASE parameter. You still also have to use CODE to give name of the .class file.

Also like IMG, APPLET has several parameters to define how it is positioned on the page. HEIGHT and WIDTH parameters work exactly as they do with IMG, specifying how big a rectangle the browser should leave for the applet. These numbers are specified in pixels. ALIGN also works exactly as for images (in those browsers that support ALIGN) defining how the applet's rectangle is placed on the page relative to other elements. Possible values include LEFT, RIGHT, TOP, TEXTTOP, MIDDLE, ABSMIDDLE, BASELINE, BOTTOM and ABSBOTTOM. Finally as with IMG you can specify an HSPACE and a VSPACE in pixels to set the amount of blank space between an applet and the surrounding text.

Finally also like IMG, APPLET has an ALT tag. As far as I know ALT is not yet implemented in any browsers. An ALT tag is used by a browser that understands the APPLET tag but for some reason cannot play the applet. For instance if an applet needs to write a file on your hard drive, but your preferences are set not to allow that, then the browser should display the ALT text.

ALT is not used for browsers that do not understand APPLET at all. For that purpose APPLET has been defined to include a closing tag as well, </APPLET>. All raw text between the opening and closing APPLET tags is ignored by a Java capable browser. However a non-Java capable browser will ignore the APPLET tags instead and read the text between them.

Passing Parameters to Applets

To demonstrate this we'll convert HelloWorldApplet into a generic string drawing applet. To do this we'll need to pass the applet parameters that define the string to be drawn.

import java.applet.Applet;    
import java.awt.Graphics; 
             
public class DrawStringApplet extends Applet {

  String input_from_page;

  public void init() {
    input_from_page = getParameter("String");
  }
  
  public void paint(Graphics g) {
    g.drawString(input_from_page, 50, 25);
  }
  
}

<HTML>
<HEAD>
<TITLE> Draw String </TITLE>
</HEAD>

<BODY>
This is the applet:<P>
<APPLET codebase="classes" code="DrawStringApplet.class" width=200 height=200><PARAM name="String" value="Howdy, there!"></APPLET>
</BODY>
</HTML>

You're not limited to one parameter either. You can pass as many named parameters to an applet as you like.

The getParameter method is straightforward. You give it a string that's the name of the parameter you want. You get back a string that's the value of the parameter. All parameters are passed as Strings. If you want to get something else like an integer then you'll need to pass it as a String and convert it into the type you really want.

The PARAM HTML tag is also straightforward. It occurs between <APPLET> and </APPLET>. It has two parameters of its own, NAME and VALUE. The NAME identifies which parameter this is for the getParameter method. VALUE is the value of the parameter as a String. Both must be enclosed in double quote marks like all other HTML tag parameters.

Events and Applets

Event Tutor Applet

import java.applet.Applet;
import java.awt.*;
              
public class EventTutor extends Applet {

  public void init() {
    System.out.println("init event");
  }
  
  public void paint(Graphics g) {
    System.out.println("paint event");
  }
    
  public void start() {
    System.out.println("start event");
  }
 
  public void destroy() {
    System.out.println("destroy event");
  }
 
  public void update(Graphics g) {
    System.out.println("update event");
  }
  
  public boolean mouseUp(Event e, int x, int y) {
    System.out.println("mouseUp event");
    return false;
  }
  
  public boolean mouseDown(Event e, int x, int y) {
   System.out.println("mouseDown event");
   return false;
  }
  
  public boolean mouseDrag(Event e, int x, int y) {
    System.out.println("mouseDrag event");
        return false;
  }
  
  public boolean mouseMove(Event e, int x, int y) {
    System.out.println("mouseMove event");
    return false;
  }
  
  public boolean mouseEnter(Event e, int x, int y) {
    System.out.println("mouseEnter event");
    return false;
  }
  
 public boolean mouseExit(Event e, int x, int y) {
    System.out.println("mouseExit event");
    return false;
  }
  
  public void getFocus() {
    System.out.println("getFocus event");
  }
  
  public void gotFocus() {
    System.out.println("gotFocus event");
  }
  
  public void lostFocus() {
    System.out.println("lostFocus event");
  }
  
  public boolean keyDown(Event e, int x) {
    System.out.println("keyDown event");
    return true;
  }
  
}

Here are some questions to answer:

1. Can you have a mouseDown event that is not followed by a mouseUp event?
2. Can you have a mouseDown event that is not followed by a mouseDrag event?
3. Can you have a mouseUp Event that is not preceded by a mouseDown event?
4. What has to happen for a paint event to occur?
5. What's the most common event? Why?
6. Are there any events you don't see?
7. How many times can you make the start event get called? the stop event?
8. Of those events you can make occur, exactly how do you do it? How many different ways can you do it?

Finally there are a whole lot of new event methods. We'll cover them in detail in the next section. For now see under what circumstances you can make each one happen.

Making a List

A List is a scrolling list of Strings defined in java.awt.List. We create a new List with new, just as we create any other Object. The specific constructor we use asks for an int that's the number of visible lines and a boolean that tells whether or not multiple selections are allowed. We'll ask for 25 lines and no multiple selections.

 List theList; 
 theList = new List(25, false);

    theList.addItem("This is a list item");

    add(theList);

import java.applet.Applet;
import java.awt.*;
              
public class EventList extends Applet {

  List theList; 

  public void init() {
    theList = new List(25, false);
    add(theList);
    theList.addItem("init event");
  }
  
  public void paint(Graphics g) {
    theList.addItem("paint event");
  }
    
  public void start() {
    theList.addItem("start event");
  }
 
  public void destroy() {
    theList.addItem("destroy event");
  }
 
  public void update(Graphics g) {
    theList.addItem("update event");
  }
  
  public boolean mouseUp(Event e, int x, int y) {
    theList.addItem("mouseUp event");
    return false;
  }
  
  public boolean mouseDown(Event e, int x, int y) {
   theList.addItem("mouseDown");
   return false;
  }
  
  public boolean mouseDrag(Event e, int x, int y) {
    theList.addItem("mouseDrag event");
        return false;
  }
  
  public boolean mouseMove(Event e, int x, int y) {
    theList.addItem("mouseMove event");
    return false;
  }
  
  public boolean mouseEnter(Event e, int x, int y) {
    theList.addItem("mouseEnter event");
    return false;
  }
  
 public boolean mouseExit(Event e, int x, int y) {
    theList.addItem("mouseExit event");
    return false;
  }
  
  public void getFocus() {
    theList.addItem("getFocus event");
  }
  
  public void gotFocus() {
    theList.addItem("gotFocus event");
  }
  
  public void lostFocus() {
    theList.addItem("lostFocus event");
  }
  
  public boolean keyDown(Event e, int x) {
    theList.addItem("keyDown event");
    return true;
  }
  
}

The Events

init

The init() method is called when your applet begins executing. Netscape is also known to call this method at other times such as when an applet is reloaded or you return to a page containing an applet. Generally you use this method to set up any data structures or perform any tasks you need to get ready to run the applet. Since it's only called once it's easy to miss the init() method in the EventTutor applet. If necessary redirect the standard output to a file and look at the first line of that file to see it.

  public void init() {
    System.out.println("init event");
  }

paint

We've already seen the paint() method. Almost any applet is going to need to override this method. This is the method in which you will do all your drawing. You can only write to the applet screen in the paint method. However there are times when you'll want to write to an offscreen image in another method and then just quickly copy that image to the screen in your paint() method.

  public void paint(Graphics g) {
    theList.addItem("paint event");
  }

stop

A stop() message says the user is no longer looking at the page that contains the applet. This is usually because the user left the page or minimized the window. At this time you should stop any CPU eating activities that don't matter when the user isn't looking at your page. For instance your Doom applet should stop tracking monster movement if the user isn't actually playing. On the other hand a spreadsheet applet in the middle of a long calculation should continue calculating because the user is likely to want the result later. Once the user returns to the page the start() method is called.

  public void stop() {
    theList.addItem("stop event");
  }

start

The start() method is called when a user brings their attention back to an applet, for instance after maximizing a window or returning to the applet's page. It is called after the init() method. Initialization code that needs to be performed every time an applet is restarted should be put here.

  public void start() {
    theList.addItem("start event");
  }

destroy

The destroy() method is called before the applet is unloaded completely. It is called after the stop() method. Users may reload the applet later, but if they do it will be as if they've never seen it before. All variables, static, member, local or otherwise will be initialized to their initial state. If you have any final cleanup to do (for instance sending output back to the httpd server) do it here.

  public void destroy() {
    theList.addItem("destroy event");
  }

update

The update() method is called automatically by the system when ????. It's often overridden when you want to use offscreen Images to avoid flicker.

  public void update(Graphics g) {
    theList.addItem("update event");
  }

mouseUp

The mouseUp() method is called whenever the mouse button is released in your applet. In most cases this is the event you'll want to watchout for, not mouseDown. A button is typically highlighted when the mouse button is pressed on it, but it is not activated till the user releases the mouse button. This gives the user a chance to change their mind by moving the cursor off the object without releasing it.

The exception would be when you want an action to continue as long as the mouse button is held down, a fast forward button on a movie playing applet for instance.

mouseUp() methods also receive the coordinates of the point where the mouse was released.

  public boolean mouseUp(Event e, int x, int y) {
    theList.addItem("mouseUp event at (" + x + "," + y + ")");
    return false;
  }

mouseDown

The mouseDown() method is called whenever the mouse button is pressed in your applet. In most cases you'll want to wait for a mouseUp before taking any action though.

mouseDown() methods also receive the coordinates of the point where the mouse was released.

  public boolean mouseDown(Event e, int x, int y) {
    theList.addItem("mouseDown event at (" + x + "," + y + ")");
    return false;
  }

mouseDrag

mouseDrag() methods occur when a user moves the mouse while holding down the mouse button. mouseDrag() methods receive the coordinates of the point where the mouse is when the event occurs.

  public boolean mouseDrag(Event e, int x, int y) {
    theList.addItem("mouseDrag event at (" + x + "," + y + ")");
        return false;
  }

mouseMove

mouseMove methods occur when a user moves the mouse without holding down the mouse button. mouseMove methods receive the coordinates of the point where the mouse is when the event occurs.

  public boolean mouseMove(Event e, int x, int y) {
    theList.addItem("mouseMove event at (" + x + "," + y + ")");
    return false;
  }

mouseEnter

Your applet receives a mouseEnter event whenever the cursor enters your applet from somewhere else. You'll also receive the coordinates of the point at which the cursor entered your applet. After this happens its typically followed by a Stream of mouseMoved events as the cursor continues through the applet so it can be hard to see.

  public boolean mouseEnter(Event e, int x, int y) {
    theList.addItem("mouseEnter event at " + x + "," + y + ")");
    return false;
  }

mouseExit

Your applet receives a mouseExit event whenever the cursor leaves your applet. You'll also receive the coordinates of the point at which the cursor exited your applet.

 public boolean mouseExit(Event e, int x, int y) {
    theList.addItem("mouseExit event at (" + x + "," + y + ")");
    return false;
  }

getFocus

  public void getFocus() {
    theList.addItem("getFocus event");
  }

gotFocus

public void gotFocus() { theList.addItem("gotFocus event"); }

lostFocus

  public void lostFocus() {
    theList.addItem("lostFocus event");
  }

keyDown

A keydown event is generated whenever the user presses a key while your applet is active. An integer keycode is returned indicating which key was pressed. As a general rule you'll want to cast this to a char to get the actual letter.

  public boolean keyDown(Event e, int x) {
    theList.addItem("The " + (char) x + " key was pressed.");
    return false;
  }

Here's the revised EventTutor Applet:

Drawing Text

Drawing Graphics: Lines, Circles, Rectangles and Colors

Drawing Rectangles

In the first applet we'll just draw a rectangle on the screen. We'll get the size of the applet as specified in the HTML file, and then we'll draw a rectangle around the applet to frame it. Here's the code:

//Draw a rectangle

import java.applet.*;    
import java.awt.*; 

public class Mondrian1 extends Applet {

  int height, width;

  public void init() {
  
    Dimension d = size();
    height = d.height;
    width = d.width;
    repaint();

  }

  public void paint(Graphics g) {

    g.drawRect(0, 0, width, height);
    
  }

}

This is called a fencepost error. The applet lives in a square 300 pixels tall by 300 pixels wide. However the upper left hand corner of the applet starts at (0, 0), not at (1, 1). This means that the applet includes the points with x and y coordinates between 0 and 299, not between 0 and 300. We drew a rectangle 301 pixels high and 301 pixels wide so the edges were chopped off.

This is fortuitous however. Not only does it allow me the opportunity to digress on fencepost errors (which, although annoying, are far less dangerous in Java than in C since Java does check array boundaries) but it also shows us something else. In Java the coordinate system for an applet begins in the upper left hand corner and increases to the right and down. This is common in computer graphics but is different from the Cartesian coordinate system where the direction of increasing y is generally assumed to be up.

Correcting the fence post error is easy. We just change g.drawRect(0, 0, width, height); to g.drawRect(0, 0, width-1, height-1);

//Draw a rectangle

import java.applet.*;    
import java.awt.*; 

public class Mondrian2 extends Applet {

  int height, width;

  public void init() {
  
    Dimension d = size();
    height = d.height;
    width = d.width;
    repaint();

  }

  public void paint(Graphics g) {

    g.drawRect(0, 0, width-1, height-1);
    
  }

}

We've introduced exactly one new statement in all this code, drawRect which is a method in the Graphics class. The line g.drawRect(0, 0, height-1, width-1) instructs the Graphics class g to draw a rectangle beginning at the point (0, 0) and ending at the point (299, 299).

This particular rectangles encompasses the entire applet's visible space. There is nothing to keep us from drawing outside the applet, in fact we did exactly that in our first version where we actually extended the rectangle to (300, 300); but anything we draw there won't be seen by the user.

The drawRect method draws an open rectangle. If we want to draw a filled rectangle we use the fillRect method. Otherwise the syntax is identical. In Mondrian3 we'll draw a filled rectangle in the center of the applet. Here's the code:

//Draw a rectangle

import java.applet.*;    
import java.awt.*; 

public class Mondrian3 extends Applet {

  int AppletHeight;
  int AppletWidth;
  int RectHeight;
  int RectWidth;
  int RectTop;
  int RectLeft;


  public void init() {
  
    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
    RectHeight = AppletHeight/3;
    RectWidth = AppletWidth/3;
    RectTop = (AppletHeight - RectHeight)/2;
    RectLeft= (AppletWidth - RectWidth)/2;
    repaint();

  }

  public void paint(Graphics g) {

    g.drawRect(0, 0, AppletWidth-1, AppletHeight-1);
    g.fillRect(RectLeft, RectTop, RectWidth-1, RectHeight-1);
    
  }

}

The extremely astute reader may object at this point. Until now we've only drawn squares. Although the last two variables passed to drawRect and fillRect must be the height and the width how do we know which is which? The simplest way to tell is to write a test program that draws a non-square rectangle. Let's try that now:

//Draw a rectangle

import java.applet.Applet;    
import java.awt.*; 

public class Mondrian4 extends Applet {

  int RectHeight, RectWidth, RectTop, RectLeft, AppletWidth, AppletHeight;

  public void init() {

    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
    RectHeight = AppletHeight/3;
    RectWidth = (AppletWidth*2)/3;
    RectTop = (AppletHeight - RectHeight)/2;
    RectLeft= (AppletWidth - RectWidth)/2;

    repaint();

  }

  public void paint(Graphics g) {

    g.drawRect(0, 0, AppletWidth-1, AppletHeight-1);
    g.fillRect(RectLeft, RectTop, RectWidth-1, RectHeight-1);

  }

}

Now that we've learned how to draw rectangles, both filled and unfilled, let's make life a little more exciting by randomly selecting the position and size of the rectangle. To do this we'll need the Math.random() method from java.lang.Math. This method returns a double between 0.0 and 1.0 so we'll need to multiply the result by the applet's height and width to get a reasonably sized rectangle that fits into our applet space. To do this we'll create the following Randomize method:

private int Randomize( int range )
{
  double  rawResult;
  
  rawResult = Math.random();
  return (int) (rawResult * range);

}

Casting in Java is safer than in C or other languages that allow arbitrary casting. Java only lets casts occur when they make sense, such as a cast between a float and an int. However you can't cast between an int and a String for example.

//Draw a rectangle

import java.applet.Applet;    
import java.awt.*; 

public class Mondrian5 extends Applet {

  int RectHeight, RectWidth, RectTop, RectLeft, AppletWidth, AppletHeight;

  public void init() {

    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
    RectTop = Randomize(AppletHeight);
    RectLeft= Randomize(AppletWidth);
    RectHeight = Randomize(AppletHeight - RectTop);
    RectWidth = Randomize(AppletWidth - RectLeft);

    repaint();

  }

  public void paint(Graphics g) {

    g.drawRect(0, 0, AppletWidth-1, AppletHeight-1);
    g.fillRect(RectLeft, RectTop, RectWidth-1, RectHeight-1);

  }
  
  
  private int Randomize(int range)
  {
    double  rawResult;

    rawResult = Math.random();
    return (int) (rawResult * range);

  }

}

Let's make our world a little more colorful. To do this we'll change the rectangle color to red. To do this we'll use a new methods setColor(), part of the Graphics class.

//Draw a colored rectangle

import java.applet.Applet;    
import java.awt.*; 

public class Mondrian6 extends Applet {

  int RectHeight, RectWidth, RectTop, RectLeft, AppletWidth, AppletHeight;

  public void init() {

    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
    RectTop = Randomize(AppletHeight);
    RectLeft= Randomize(AppletWidth);
    RectHeight = Randomize(AppletHeight - RectTop);
    RectWidth = Randomize(AppletWidth - RectLeft);

    repaint();

  }

  public void paint(Graphics g) {

   // g.setBackground(Color.white);
    g.setColor(Color.red);
    g.drawRect(0, 0, AppletWidth-1, AppletHeight-1);
    g.fillRect(RectLeft, RectTop, RectWidth-1, RectHeight-1);

  }
  
  
  private int Randomize(int range)
  {
    double  rawResult;

    rawResult = Math.random();
    return (int) (rawResult * range);

  }

}

• black
• blue
• cyan
• darkGray
• gray
• green
• lightGray
• magenta
• orange
• pink
• red
• white
• yellow

By using the color constructor we can expand our program to select not only a random rectangle but also a random color for the rectangle. Here's the code:

//Draw a randomly colored rectangle

import java.applet.Applet;    
import java.awt.*; 

public class Mondrian7 extends Applet {

  int RectHeight, RectWidth, RectTop, RectLeft, AppletWidth, AppletHeight;
  Color RectColor;

  public void init() {

    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
    RectTop = Randomize(AppletHeight);
    RectLeft= Randomize(AppletWidth);
    RectHeight = Randomize(AppletHeight - RectTop);
    RectWidth = Randomize(AppletWidth - RectLeft);
    RectColor = new Color(Randomize(255),Randomize(255),Randomize(255));

    repaint();

  }

  public void paint(Graphics g) {

   // g.setBackground(Color.white);
    g.setColor(RectColor);
    g.drawRect(0, 0, AppletWidth-1, AppletHeight-1);
    g.fillRect(RectLeft, RectTop, RectWidth-1, RectHeight-1);

  }
  
  
  private int Randomize(int range)
  {
    double  rawResult;

    rawResult = Math.random();
    return (int) (rawResult * range);

  }

}

//Draw many randomly colored rectangles

import java.applet.Applet;    
import java.awt.*; 

public class Mondrian8 extends Applet {

  int RectHeight, RectWidth, RectTop, RectLeft, AppletWidth, AppletHeight;
  Color RectColor;
  int numberRectangles = 100;
  
  public void init() {

    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;

    repaint();

  }

  public void paint(Graphics g) {
  
    g.setColor(Color.black);
    g.drawRect(0, 0, AppletWidth-1, AppletHeight-1);
   
    for (int i=0; i < numberRectangles; i++)  {
      RectTop = Randomize(AppletHeight);
      RectLeft= Randomize(AppletWidth);
      RectHeight = Randomize(AppletHeight - RectTop);
      RectWidth = Randomize(AppletWidth - RectLeft);
      RectColor = new Color(Randomize(255),Randomize(255),Randomize(255));
      g.setColor(RectColor);
      g.fillRect(RectLeft, RectTop, RectWidth-1, RectHeight-1);
  }
  
 }
  
  
  private int Randomize(int range)
  {
    double  rawResult;

    rawResult = Math.random();
    return (int) (rawResult * range);

  }

}

//Draw many random rectangles

import java.applet.Applet;    
import java.awt.*; 

public class Mondrian9 extends Applet {

  int RectHeight, RectWidth, RectTop, RectLeft, AppletWidth, AppletHeight;
  Color RectColor;
  int numberRectangles = 100;
  
  public void init() {

    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
    String s = getParameter("Number");
    if (s != null) {
      numberRectangles = Integer.valueOf(s).intValue();
  }
  
    repaint();

  }

  public void paint(Graphics g) {
  
    g.setColor(Color.black);
    g.drawRect(0, 0, AppletWidth-1, AppletHeight-1);
   
    for (int i=0; i < numberRectangles; i++)  {
      RectTop = Randomize(AppletHeight);
      RectLeft= Randomize(AppletWidth);
      RectHeight = Randomize(AppletHeight - RectTop);
      RectWidth = Randomize(AppletWidth - RectLeft);
      RectColor = new Color(Randomize(255),Randomize(255),Randomize(255));
      g.setColor(RectColor);
      g.fillRect(RectLeft, RectTop, RectWidth-1, RectHeight-1);
  }
  
 }
  
  
  private int Randomize(int range)
  {
    double  rawResult;

    rawResult = Math.random();
    return (int) (rawResult * range);

  }

}

Exercises

1. For the artistically inclined: write a version of Mondrian that draws pictures that are more believably in the style of Piet Mondrian. You should probably restrict your color choices and not allow rectangles to overlap.

Drawing Lines

import java.applet.Applet;    
import java.awt.*; 

public class SimpleLine extends Applet {

  int AppletHeight, AppletWidth;

  public void init() { 
    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
  }

 public void paint(Graphics g) {
 
    g.drawLine(0, 0, AppletWidth, AppletHeight);
  
 }

}

Graphing Functions

We begin with the skeleton applet. We'll need to add some code to the paint method of the applet to make it draw something. Let's begin by drawing a sine wave from the left hand side of the image to the right hand side. Here's the complete program:

import java.applet.*;    
import java.awt.*; 
              
public class GraphApplet extends Applet {

  int x0, xN, y0, yN;

  public void init() {
    // How big is the applet?
    Dimension d = size();
  
    x0 = 0;
    xN = d.width-1;
    y0=0;
    yN=d.height-1;
  }
  
  public void paint(Graphics g) {

    for (int x = x0; x < xN; x++) {
      g.drawLine(x,(int) (yN*Math.sin(x)),x+1, (int) (yN*Math.sin(x+1)));
    }

  }
  
}

    for (int x = x0; x < xN; x++) {
      g.drawLine(x,(int) (yN*Math.sin(x)),x+1, (int) (yN*Math.sin(x+1)));
    }

This applet runs but it's got a lot of problems. All of them can be related to two factors:

1. Sines are floating point operations. To do a really useful graphing applet we need to be able to use floating point numbers.

2. The coordinate system of an applet counts from (0,0) at the upper left hand corner to the right and down. The standard Cartesian coordinate system we expect graphs to use counts from (0,0) in the lower left hand corner to the right and up. The origin can be moved in both systems, for instance to the center of the applet, but we still need to transform between the y down and the y up coordinates.

We'll need a method that will convert a point in the applet window into a point in the Cartesian plane, and one that will convert it back. Here it is:

import java.applet.*;    
import java.awt.*; 
              
public class GraphApplet extends Applet {

  int x0, xN, y0, yN;
  double xmin, xmax, ymin, ymax;
  int AppletHeight, AppletWidth;

  public void init() {
    // How big is the applet?
    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth  = d.width;
    x0 = 0;
    xN = AppletWidth-1;
    y0=0;
    yN=AppletHeight-1;
    xmin = -10.0;
    xmax =  10.0;
    ymin = -1.0;
    ymax =  1.0;
  }
  
  public void paint(Graphics g) {
  
    double x1,y1,x2,y2;
    int i, j1, j2;

    j1 = yvalue(0);
    for (i = 0; i < AppletWidth; i++) {
      j2 = yvalue(i+1);
      g.drawLine(i, j1 ,i+1, j2);
      j1 = j2;
    }

  }
  
  private int yvalue(int ivalue)  {
  
    // Given the  xpoint we're given calculate the Cartesian equivalent
    double x, y;
    int jvalue;
    
    x = (ivalue * (xmax - xmin)/(AppletWidth - 1)) + xmin;
    
    // Take the sine of that x 
    y = Math.sin(x);
    
    // Scale y into window coordinates
    jvalue = (int) ((y - ymin)*(AppletHeight - 1)/(ymax - ymin));
  
    // Switch jvalue from cartesian coordinates to computer graphics coordinates    
    jvalue = AppletHeight - jvalue;
    
    return jvalue;
  
  }


  
}

import java.applet.*;    
import java.awt.*; 
              
public class GraphApplet extends Applet {

  int x0, xN, y0, yN;
  double xmin, xmax, ymin, ymax;
  int AppletHeight, AppletWidth;

  public void init() {
    String ParamString;
  
    // How big is the applet?
    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth  = d.width;
    x0 = 0;
    xN = AppletWidth-1;
    y0=0;
    yN=AppletHeight-1;    

    ParamString = getParameter("xmin");
    if (ParamString != null) {
      xmin = Double.valueOf(ParamString).doubleValue();
    }
    else {
      xmin = -1.0;
    }
    ParamString = getParameter("xmax");
    if (ParamString != null) {
      xmax = Double.valueOf(ParamString).doubleValue();
    }
    else {
      xmax = 1.0;
    }
    ParamString = getParameter("ymax");
    if (ParamString != null) {
      ymax = Double.valueOf(ParamString).doubleValue();
    }
    else {
      ymax = 1.0;
    }
    ParamString = getParameter("ymin");
    if (ParamString != null) {
      ymin = Double.valueOf(ParamString).doubleValue();
    }
    else {
      ymin = -1.0;
    }
  }

  public void paint(Graphics g) {
  
    double x1,y1,x2,y2;
    int i, j1, j2;

    j1 = yvalue(0);
    for (i = 0; i < AppletWidth; i++) {
      j2 = yvalue(i+1);
      g.drawLine(i, j1 ,i+1, j2);
      j1 = j2;
    }

  }
  
  private int yvalue(int ivalue)  {
  
    // Given the  xpoint we're given calculate the Cartesian equivalent
    double x, y;
    int jvalue;
    
    x = (ivalue * (xmax - xmin)/(AppletWidth - 1)) + xmin;
    
    // Take the sine of that x 
    y = Math.sin(x);
    
    // Scale y into window coordinates
    jvalue = (int) ((y - ymin)*(AppletHeight - 1)/(ymax - ymin));
  
    // Switch jvalue from cartesian coordinates to computer graphics coordinates    
    jvalue = AppletHeight - jvalue;
    
    return jvalue;
  
  }
  
}

So far we've only graphed sine functions. It should be obvious how to modify the code to graph cosines or many other kinds of functions. However what if we want to define the function at runtime?

Exercises

1. Add labeled coordinate axes to the graph.

2. Our graph method handled mathematical functions. How would you need to change it and what features would you add to make it suitable for plotting discrete experimental data?

An infinite set that with zero length

The middle third set is defined by starting with all the real numbers between zero and one inclusive. Then we cut out the middle third of that set (exclusive of the endpoints). i.e. everything between one third and two thirds exclusive.

Next we cut the middle third of the two line segments that remain, i.e. everything between one ninth and two ninths and between seven ninths and eight ninths. We continue this process indefinitely.

Was that confusing? Good. A picture is worth a thousand words and a good Java program is worth a thousand pictures. We now proceed to show you a Java program that draws successive pictures to demonstrate the middle third set.

import java.applet.Applet;    
import java.awt.*;
import java.util.Vector;

public class MiddleThird extends Applet {

int AppletWidth;
int AppletHeight;

Vector endpoints = new Vector();

  public void init() { 
    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
    endpoints.addElement(new Float(0.0f));
    endpoints.addElement(new Float(1.0f));  
  }

 public void paint(Graphics g) {
 
   float x1, x2;
   Float tempFloat;
   for (int i = 0; i <  AppletHeight; i+= 5) {
     // draw the lines
     for (int j=0; j < endpoints.size(); j += 2) {
       tempFloat = (Float) endpoints.elementAt(j);
       x1 = tempFloat.floatValue();
       tempFloat = (Float) endpoints.elementAt(j+1);
       x2 = tempFloat.floatValue();
       g.drawLine( Math.round(x1*AppletWidth), i, Math.round(x2*AppletWidth), i);
     }
     //remove the middle third of the lines
     CutSegments();
     // Now check to see if we've exceeded the resolution of our screen
     tempFloat = (Float) endpoints.elementAt(0);
     x1 = tempFloat.floatValue();
     tempFloat = (Float) endpoints.elementAt(1);
     x2 = tempFloat.floatValue();
     if (Math.round(x1*AppletWidth) == Math.round(x2*AppletWidth)) break;
   }
  
   
 }

 private void CutSegments() {

   int index = 0;
   float gap;
   float x1, x2;
   Float tempFloat1, tempFloat2;
   int stop = endpoints.size();
   
   for (int i=0; i < stop; i+=2) {
      CutMiddleThird(index, index+1);
      index += 4;
   }
   
 }
 
 
  private void CutMiddleThird(int left, int right) {

   float gap;
   float x1, x2;
   Float tempFloat1, tempFloat2;
   
   tempFloat1 = (Float) endpoints.elementAt(left);
   tempFloat2 = (Float) endpoints.elementAt(right);
   gap = tempFloat2.floatValue() - tempFloat1.floatValue();
   x1  = tempFloat1.floatValue() + gap/3.0f;
   x2  = tempFloat2.floatValue() - gap/3.0f;
   endpoints.insertElementAt(new Float(x2), right);
   endpoints.insertElementAt(new Float(x1), right);
   
 }

}

Flying Lines

//Bounce lines around in a box

import java.applet.Applet;    
import java.awt.*; 
        
public class FlyingLines extends Applet {

  int NUM_LINES = 25;
  int gDeltaTop=3, gDeltaBottom=3;
  int gDeltaLeft=2, gDeltaRight=6;
  int AppletWidth, AppletHeight;
  int gLines[][] = new int[NUM_LINES][4];

  public void init() {

    AppletWidth = size().width;
    AppletHeight = size().height;

  }
  
  public void start() {
    gLines[0][0] = Randomize(AppletWidth);
    gLines[0][1] = Randomize(AppletHeight);
    gLines[0][2] = Randomize(AppletWidth);
    gLines[0][3] = Randomize(AppletHeight);
    for (int i=1; i < NUM_LINES; i++ ) {
      LineCopy(i, i-1);
      RecalcLine(i);
    } 
    repaint();
  
  }

  public void paint(Graphics g) {

     while (true) {
      for (int i=NUM_LINES - 1; i > 0; i--) {
        LineCopy(i, i-1);
      }
      RecalcLine(0);
      g.setColor(Color.black);
      g.drawLine(gLines[0][0], gLines[0][1], gLines[0][2], gLines[0][3]);
      g.setColor(getBackground());
      g.drawLine(gLines[NUM_LINES-1][0], gLines[NUM_LINES-1][1], 
        gLines[NUM_LINES-1][2], gLines[NUM_LINES-1][3]);
    }
    
  }

  private void LineCopy (int to, int from)  {

    for (int i = 0; i < 4; i++) {
      gLines[to][i] = gLines[from][i];
    }

  }

  public int Randomize( int range ) {
    double  rawResult;

    rawResult = Math.random();
    return (int) (rawResult * range);

  }

  private void RecalcLine( int i ) {

    gLines[i][1] += gDeltaTop;
    if ((gLines[i][1] < 0) || (gLines[i][1] > AppletHeight)) {
      gDeltaTop *= -1;
      gLines[i][1] += 2*gDeltaTop;
    }

    gLines[i][3] += gDeltaBottom;
    if ( (gLines[i][3] < 0) || (gLines[i][3] > AppletHeight) ) {
      gDeltaBottom *= -1;
      gLines[i][3] += 2*gDeltaBottom;
    }

    gLines[i][0] += gDeltaLeft;
    if ( (gLines[i][0] < 0) || (gLines[i][0] > AppletWidth) ) {
      gDeltaLeft *= -1;
      gLines[i][0] += 2*gDeltaLeft;
    }

    gLines[i][2] += gDeltaRight;
    if ( (gLines[i][2] < 0) ||  (gLines[i][2] > AppletWidth) ) {
      gDeltaRight *= -1;
      gLines[i][2] += 2*gDeltaRight;
    }
    
  }  //RecalcLine ends here

} // FlyingLines ends here

Taking Action: Threads

The paint loops in both Mondrian and FlyingLines are ideal for a thread, a separate stream of execution that takes place simultaneously and independently of everything else that might be happening (like responding to the programmer's insistence to "Quit!, Damnit!"). Without threads an entire program can be held up by one CPU intensive task or, as in Flying Lines, one infinite loop, intentional or otherwise.

As a general rule all CPU intensive tasks should be placed in their own threads. Here's one way to do it.

//Draw infinitely many random rectangles

import java.applet.Applet;    
import java.awt.*; 

public class ThreadedMondrian extends Applet implements Runnable {

  int RectHeight, RectWidth, RectTop, RectLeft, AppletWidth, AppletHeight;
  Color RectColor;
  Thread kicker = null;
  int pause;
  
  public void init() {

    Dimension d = size();
    AppletHeight = d.height;
    AppletWidth = d.width;
    repaint();
  }

  public void paint(Graphics g) {
  
    g.setColor(Color.black);
    g.drawRect(0, 0, AppletWidth-1, AppletHeight-1);
   
    for (int i=0; i < 10; i++) {
      RandomRect();
      g.setColor(RectColor);
      g.fillRect(RectLeft, RectTop, RectWidth-1, RectHeight-1);
    } 
  
 }
  
  public void run() {
    Thread.currentThread().setPriority(Thread.MIN_PRIORITY);

    while (true) {  // infinite loop
      repaint();
      try {
        Thread.sleep(100);
       }
       catch (Exception e) {
       
       }
    }
  }

  public void start() {
    if (kicker == null) {
      kicker = new Thread(this);
      kicker.start();
    }
  }

  public void stop() {
    kicker = null;
  }

  public void RandomRect()  {
      RectTop   = Randomize(AppletHeight);
      RectLeft  = Randomize(AppletWidth);
      RectHeight= Randomize(AppletHeight - RectTop);
      RectWidth = Randomize(AppletWidth - RectLeft);
      RectColor = new Color(Randomize(255),Randomize(255),Randomize(255));
  }

  private int Randomize(int range)
  {
    double  rawResult;

    rawResult = Math.random();
    return (int) (rawResult * range);

  }

}

1. We specified that our applet implements Runnable.
2. We added a run method.
3. We added a start method.
4. We added a stop method.

Let's look at them in more detail:

Our applet implements Runnable

Run Method

Start Method

Stop Method

//Bounce lines around in a box

import java.applet.Applet;    
import java.awt.*; 
        
public class FlyingLines extends Applet implements Runnable {

  int NUM_LINES = 25;
  int gDeltaTop=3, gDeltaBottom=3;
  int gDeltaLeft=2, gDeltaRight=6;
  int AppletWidth, AppletHeight;
  int gLines[][] = new int[NUM_LINES][4];

  public void init() {

    AppletWidth = size().width;
    AppletHeight = size().height;

  }
  
  public void start() {
    gLines[0][0] = Randomize(AppletWidth);
    gLines[0][1] = Randomize(AppletHeight);
    gLines[0][2] = Randomize(AppletWidth);
    gLines[0][3] = Randomize(AppletHeight);
    for (int i=1; i < NUM_LINES; i++ ) {
      LineCopy(i, i-1);
      RecalcLine(i);
    } 
    repaint();
    Thread t = new Thread(this);
    t.start();
  
  }

  public void run () {
  
    Thread.currentThread().setPriority(Thread.MIN_PRIORITY);
  
    while (true) {
      for (int i=NUM_LINES - 1; i > 0; i--) {
        LineCopy(i, i-1);
      }
      RecalcLine(0);
      System.out.println(gLines[0][0] + ", " + gLines[0][1] + "," + gLines[0][2] + ", " + gLines[0][3]);
      repaint();
      try {
        Thread.currentThread().sleep(10);
      }
      catch (Exception e) {
      
      }
    }
  
  }

  public void paint(Graphics g) {

    for (int i=0; i < NUM_LINES; i++) {
      g.drawLine(gLines[i][0], gLines[i][1], gLines[i][2], gLines[i][3]);
    }
    
  }

  private void LineCopy (int to, int from)  {

    for (int i = 0; i < 4; i++) {
      gLines[to][i] = gLines[from][i];
    }

  }

  public int Randomize( int range ) {
    double  rawResult;

    rawResult = Math.random();
    return (int) (rawResult * range);

  }

  private void RecalcLine( int i ) {

    gLines[i][1] += gDeltaTop;
    if ((gLines[i][1] < 0) || (gLines[i][1] > AppletHeight)) {
      gDeltaTop *= -1;
      gLines[i][1] += 2*gDeltaTop;
    }

    gLines[i][3] += gDeltaBottom;
    if ( (gLines[i][3] < 0) || (gLines[i][3] > AppletHeight) ) {
      gDeltaBottom *= -1;
      gLines[i][3] += 2*gDeltaBottom;
    }

    gLines[i][0] += gDeltaLeft;
    if ( (gLines[i][0] < 0) || (gLines[i][0] > AppletWidth) ) {
      gDeltaLeft *= -1;
      gLines[i][0] += 2*gDeltaLeft;
    }

    gLines[i][2] += gDeltaRight;
    if ( (gLines[i][2] < 0) ||  (gLines[i][2] > AppletWidth) ) {
      gDeltaRight *= -1;
      gLines[i][2] += 2*gDeltaRight;
    }
    
  }  //RecalcLine ends here

} // FlyingLines ends here

Bozo Sort

class BozoSortAlgorithm extends SortAlgorithm {

  void sort(int a[]) {
    
    boolean sorted = false;
    
    while (!sorted) {
      int index1 = Randomize(a.length);
      int index2 = Randomize(a.length);  
     
      int temp = a[index2];
      a[index2] = a[index1];
      a[index1] = temp;
      // Is a[] sorted?
      sorted = true;
      for (int i = 1; i < a.length; i++)  {
        if (a[i-1] > a[i]) {
          sorted = false;
          break;
        }  // end if
      }  // end for
    } // end while
  }  // end sort 
   
  private int Randomize( int range )  {

    double  rawResult;
  
    rawResult = Math.random();
    return (int) (rawResult * range);

  }
  
}  // end BozoSortAlgorithm

Interaction: Mouse and Keyboard Input

Mouse Input: Java Doodle

import java.applet.Applet;
import java.awt.*;
import java.util.Vector;

public class JavaDoodle extends Applet {

  Vector points = new Vector();

  
  public void paint(Graphics g) {
  
  	int x1, y1, x2, y2;
  	Point tempPoint;
  
    if (points.size() > 1) {
      tempPoint = (Point) points.elementAt(0);
	  x1 = tempPoint.x;
	  y1 = tempPoint.y;
      for (int i = 1; i < points.size(); i++) {
    	tempPoint = (Point) points.elementAt(i);
	  	x2 = tempPoint.x;
	  	y2 = tempPoint.y;
    	g.drawLine(x1, y1, x2, y2);
    	x1 = x2;
    	y1 = y2;
      } // end for
    } // end if
  }
  
  public boolean mouseDown(Event e, int x, int y) {
    points.addElement(new Point(x, y));
  	return true;
  }

  public boolean mouseDrag(Event e, int x, int y) {
    points.addElement(new Point(x, y));
    repaint();
  	return true;
  }

  public boolean mouseUp(Event e, int x, int y) {
    points.addElement(new Point(x, y));
    repaint();
  	return true;
  }



}

Exercises

1. Revise the applet so that it doesn't draw a line between the point where the mouse button was released and the point where it was pressed again.

Keyboard Input: TypeWriter

import java.applet.Applet;    
import java.awt.Event; 
import java.awt.Graphics; 

public class typewriter extends Applet {

  int numcols = 80;
  int numrows = 25;
  int row = 0;
  int col = 0;
  char page[][] = new char[numrows][];

  public void init() {

        for (int i = 0; i < numrows; i++) {
      page[i] = new char[numcols];
    }
    for (int i = 0; i < numrows; i++) {
    	for (int j = 0; j < numcols; j++) {
    	  page[i][j] = '\0';
    	}
    }

  }
  
  
  public boolean keyDown(Event e, int key) {
 
    char c = (char) key;

    switch (key) {
      case Event.HOME:
        row = 0;
        col = 0;
        break;
      case Event.END:
        row = numrows-1;
        col = numcols-1;
        break;
      case Event.UP:
        if (row > 0) row--;
        break;
      case Event.DOWN:
        if (row < numrows-1) row++;
        break;
      case Event.LEFT:
        if (col > 0) col--;
        else if (col == 0 && row > 0) {
          row--;
          col=numcols-1;
        }
        break;
      case Event.RIGHT:
        if (col < numcols-1) col++;
        else if (col == numcols-1 &&  row < numrows-1) {
          row++;
          col=0;
        }
        break;
      default:
        if (c == '\n' || c == '\r') {
          row++;
          col = 0;
        }
        else if (row < numrows) {
          if (col >= numcols) {
    	    col = 0;
    	    row++;
          }
          page[row][col] = c;
          col++;
        }
   	    else { // row >= numrows
   	     col++;
   	    }
   	 }
   	 repaint();
   	 return true;
  } 


  public void paint(Graphics g) {

	for (int i=0; i < numrows; i++) {
	  String tempString = new String(page[i]);	      
      g.drawString(tempString, 5, 15*(i+1));
    }
    
  }

}

Part 4: Objects, Classes, Methods, and Interfaces

What is Object Oriented Programming?

The History of Programming

As computers grew in power and memory, it was no longer possible for a programmer to keep track of what was happening at every location in the machine's physical memory. Card readers and assembly language were invented to make programming more feasible. In assembly language the programmer uses mnemonic codes like MOV to represent particular bit sequences. These codes mapped directly to individual instructions on the CPU, and memory was still addressed directly. One code meant exactly one CPU instruction. (More modern assembly languages don't always map as directly to the CPU as the older ones did.) Algorithmically The philosophy of "Use whatever works" continued.

Assembly language was still a bear to deal with, especially as related to arrays and storage in memory. Therefore the first high-level programming language, Fortran, was invented to spare programmers from the pains of dealing with keeping track of the location of their variables in memory. (It's interesting to note that this lesson has had to be learned again and again and again. The buggiest parts of C and C++ programs result from programmers being allowed to access arbitrary bytes of memory. Java has wisely removed this capability. 99 times out of a 100 you don't need it. A large part of training a C or C++ programmer to use Java, consists of convincing them of this fact.). Fortran was the first example of a third-generation language. In a third generation language you tell the computer the algorithms and data structures it should use to calculate the results you want; but you use more abstract logical and mathematical operators rather than directly manipulating addresses in memory and CPU instructions. In a third generation language, statements represent several machine instructions. Which instructions they represent may even depend on their context.

These languages may be compiled or interpreted. In either case your program code needs to be translated into equivalent machine instructions. This level of abstraction made considerably more powerful algorithms and data structures possible.

Java is a very advanced third generation language. Most of the other computer languages you're probably familiar with, Fortran, Basic, C, C++, Cobol, Pascal, as well as most of the one's you're not familiar with (AppleScript, Frontier, Eiffel, Modula-3, ADA, PL/I, etc.) are also third-generation languages (or 3GL's for short).

When third generation languages were invented, they were supposed to make computers so easy to use even the CEO could write programs. This turned out not to be true. Fourth generation languages (or 4GL's for short) moved the abstraction level a step higher. In these languages you tell the computer what results you want rather telling it how to calculate those results. For instance you would ask for the total sales for the year, without specifying the loops necessary to sum all the sales of all the salespeople. SQL is the most popular fourth generation language.

Of all these languages there's no question that 3GL's have been the most successful by almost any measure. A number of different styles of 3GL programming and programming languages have sprung up, most learning from the experience and mistakes of its predecessors. Fortran (and its cousin Basic) were the first. They shared with assembly language an attitude of "Whatever works, no matter how ugly." They had limited flow control (essentially for loops and goto statements) and one data structure, the array. All variables were global and it was impossible to hide one part of the program from any other. Although it was possible to write maintainable, legible code in these languages, few people did.

Pascal and C were the next widely successful languages. They made possible a style of programming known as structured programming. Structured programming languages have many different flow control constructs (switch statements, while loops, and more) as well as tools for more complicated data structures (structs, records and pointers). Goto is deprecated in structured programming though not eliminated entirely. (It is still necessary for some error handling.) Finally they have subroutines with local variables that are capable of splitting the code into more manageable and understandable chunks. These languages proved more capable of writing larger, more maintainable programs. However they too began to bog down when faced with the need to share code among programmers and to write very large (greater than 50,000 line) programs.

Some of the above history may sound a little funny to those of you with experience in the languages I'm discussing. After all Basic has subroutines and local variables, doesn't it? The fact is successful computer languages have continued to evolve. Fortran now has pointers so it can create more complicated data structures. Basic has while loops. Cobol has objects. And on some architectures like Alpha/VMS the assembly language bears little to no resemblance to the underlying machine architecture. These features were not parts of the first versions of the language, however. And despite these improvements the modern versions of these languages are their parents children. Basic and Fortran programmers still often produce spaghetti code. Assembly language is quick to run but long to program. C is obfuscated beyond the comprehension of mere mortals.

The third generation of 3GL's (3.3 GL's) began to take hold in the late 80's. These were the object oriented languages. Although object oriented languages had been around since the late 1960's, it wasn't until the late 80's that computer hardware became fast enough and memory cheap enough to support them. (Object oriented programming is not a panacea. It exacts a speed penalty over plain vanilla C or Fortran code, and often requires twice as much memory.)

Object oriented languages (OOP for short) included all the features of structured programming and added still more powerful ways to organize algorithms and data structures. There are three key features of OOP languages: encapsulation, polymorphism and inheritance. All of them are tied to the notion of a class.

Classes and Objects

Programming languages provide a number of simple data types like int, float and String. However very often the data you want to work with may not be simple ints, floats or Strings. Classes let programmers define their own more complicated data types.

For instance let's suppose your program needs to keep a database of web sites. For each site you have a name, a URL, and a description. In traditional programming languages you'd have three different String variables for each web site. With a class you combine these into one package like so:

class website {

  String name;
  String url;
  String description;

}

In our web site database we will have many thousands of websites. Each specific web site is an object. The definition of a web site though, which we gave above, is a class. This is a very important distinction. A class defines what an object is, but it is not itself an object. An object is a specific instance of a class. Thus when we create a new object we say we are instantiating the object. Each class exists only once in a program, but there can be many thousands of objects that are instances of that class.

To instantiate an object in Java we use the new operator. Here's how we'd create a new web site:

    website x = new website();

    website x = new website();
    
    x.name = "Cafe Au Lait";
    x.url = "http://metalab.unc.edu/javafaq/";
    x.description = "Really cool!";
    
    System.out.println(x.name + " at " + x.url + " is " + x.description);

Methods

class website {

  String name;
  String url;
  String description;
  
  print() {
    System.out.println(name + " at " + url + " is " + description);
  }

}

    website x = new website();
    
    x.name = "Cafe Au Lait";
    x.url = "http://metalab.unc.edu/javafaq/";
    x.description = "Really cool!";
    
    x.print();

The print() method is completely enclosed within the website class. All methods in Java must belong to a class. Unlike C++ programs, Java programs cannot have a method hanging around in global space that does everything you forgot to do in your classes.

Constructors

class website {

  String name;
  String url;
  String description;
  
  public website() {
    name = ""; 
    url  = "";
    description = "";
  }

}

class website {

  String name;
  String url;
  String description;
  
  public website(String n, String u, String d) {
    name = n; 
    url  = u;
    description = d;
  }

}

    website x = new website("Cafe Au Lait", "http://metalab.unc.edu/javafaq/", "Really cool!");
    x.print();

However what if sometimes when we want to create a web site we know the URL, name, and description, and sometimes we don't? Best of all, let's use both!

class website {

  String name;
  String url;
  String description;
  
  public website(String n, String u, String d) {
    name = n; 
    url  = u;
    description = d;
  }

  public website() {
    name = ""; 
    url  = "";
    description = "";
  }

}

If you have one or two or four String arguments to the constructor, or arguments that aren't Strings, then the compiler generates an error because it doesn't have a method whose signature matches the requested method call.

toString Methods

public class ClassTest {

  public static void main(String args[]) {
  
    website x = new website("Cafe Au Lait", "http://metalab.unc.edu/javafaq/", "Really cool!");
    System.out.println(x);
  
  }

}


class website {

  String name;
  String url;
  String description;
  
  public website(String n, String u, String d) {
    name = n; 
    url  = u;
    description = d;
  }

  public website() {
    name = ""; 
    url  = "";
    description = "";
  }
  
  public String toString() {
    return  (name + " at " + url + " is " + description);
  }

}

Some Advocacy

Java is the latest and possibly the greatest third generation programming language. Here I need to explain why Java is a better OOP language than C++.

A Non-Trivial Examples: Complex Numbers

public class ComplexNumber extends Object {

  public double u;
  public double v;

}

We also have to write code to explicitly add the numbers, multiply them or do anything else we might need to do with complex numbers. If we need to add complex numbers in more than one place, then we need to write the addition code again, or, at the very least, copy and paste it.

A better implementation of a complex number class will shield us from the exact storage of the data, i.e. x and y vs. r and theta. It will also provide methods that let us perform any operation we might need to perform on or with a complex number.

Before writing code we need to ask ourselves what we'll do with a complex number. Most objects first require a constructor, a method that is called when you create a new complex number. A more complicated object may also require a destructor method that's called when you get rid of an object; but since this is a fairly simple object, we'll let Java's built-in garbage collection take care of that for us.

Since these are complex numbers it's not unlikely that we'll need to add them, subtract them, multiply them and divide them. We'll also want to be able to access their real and imaginary parts as well as their absolute values and arguments. The following class does all that.

//
public class Complex extends Object {

  private double u;
  private double v;

  Complex (double x, double y) {

    u=x;
    v=y;

  }

  public double Real () {

    return u;

  }

  public double Imaginary () {

    return v;

  }

  public double Magnitude () {

    return Math.sqrt(u*u + v*v);

  }

  public double Arg () {

    return Math.atan2(v, u);

  }

  // Add z to w; i.e. w += z
  public Complex Plus (Complex z) {

    
    return new Complex(u + z.u, v + z.v);

  }

  // Subtract z from w
  public Complex Minus (Complex z) {

    return new Complex(u - z.u, v - z.v);

  }

  public Complex Times (Complex z) {

    return new Complex(u*z.u - v*z.v, u*z.v + v*z.u);
    
  }


  // divide w by z
  public Complex DivideBy (Complex z) {

    double rz = z.Magnitude(); 

    return new Complex((u * z.u + v * z.v)/(rz*rz),(v * z.u - u * z.v)/(rz*rz));

  }

}

The use of one of these methods will look like the following. Add the following ComplexExamples class to the Complex.java file and compile. Then run ComplexExamples in the usual way by typing java ComplexExamples.

//Complex Arithmetic Examples
class ComplexExamples  {

  public static void main (String args[]) {
  
    Complex u, v, w, z;

    u = new Complex(1,2);
    System.out.println("u: " + u.Real() + " + " + u.Imaginary() + "i");
    v = new Complex(3,-4.5);
    System.out.println("v: " + v.Real() + " + " + v.Imaginary() + "i");
    
    // Add u + v;
    z=u.Plus(v);
    System.out.println("u + v: "+ z.Real() + " + " + z.Imaginary() + "i");
    // Add v + u;
    z=v.Plus(u);
    System.out.println("v + u: "+ z.Real() + " + " + z.Imaginary() + "i");

    z=u.Minus(v);
    System.out.println("u - v: "+ z.Real() + " + " + z.Imaginary() + "i");
    z=v.Minus(u);
    System.out.println("v - u: "+ z.Real() + " + " + z.Imaginary() + "i");

    z=u.Times(v);
    System.out.println("u * v: "+ z.Real() + " + " + z.Imaginary() + "i");
    z=v.Times(u);
    System.out.println("v * u: "+ z.Real() + " + " + z.Imaginary() + "i");

    z=u.DivideBy(v);
    System.out.println("u / v: "+ z.Real() + " + " + z.Imaginary() + "i");
    z=v.DivideBy(u);
    System.out.println("v / u: "+ z.Real() + " + " + z.Imaginary() + "i");

  }

}

Exercises

1. What happens if we try to add a complex number to itself? e.g.

   
   z = u.Add(u);
   

   How about if we multiply, divide or subtract? e.g.

   
   z = u.Multiply(u);
   z = u.Divide(u);
   z = u.Minus(u);
   

2. Rewrite the Complex class so that it stores its data as r and theta rather than u and v. Be sure to be careful at zero.
3. Add PlusEqual, MinusEqual, DivideEqual and MultiplyEqual methods to the Complex class that mimic the behavior of the +=, -=, *= and /= operators.
4. Add an equality method to the Complex class that tests whether two complex numbers are equal and returns a boolean.
5. For math whizzes only: Explain why it would not be a good idea to add less than or greater than methods to the Complex class.
6. For math whizzes only: Add a logarithm method to the Complex number class. Pick the branch between zero and 2pi.
7. For math whizzes only: Add a power method to the complex number class. This is straightforward for real powers. For a real challenge allow arbitrary complex powers. Be sure to consider how you'll deal with branch cuts.

toString Methods

System.out.println(u);

instead? It turns out we can. All objects have a toString method which is inherited from the Object class. However the default toString() method isn't very useful so we want to override it with one of our own creation that handles the conversion to complex numbers. Add the following method to the Complex class:

  public String toString() {
  
    if (v >= 0) return (String.valueOf(u) + " + " + String.valueOf(v) + "i");
    else return (String.valueOf(u) + " - " + String.valueOf(-v) + "i");
  }

class ComplexExamples  {

  public static void main (String args[]) {
  
    Complex u, v, z;

    u = new Complex(1,2);
    System.out.println("u: " + u);
    v = new Complex(3,-4.5);
    System.out.println("v: " + v);
    
    // Add u + v;
    z=u.Plus(v);
    System.out.println("u + v: " + z);
    // Add v + u;
    z=v.Plus(u);
    System.out.println("v + u: " + z);


    z=u.Minus(v);
    System.out.println("u - v: " + z);
    z=v.Minus(u);
    System.out.println("v - u: " + z);

    z=u.Times(v);
    System.out.println("u * v: " + z);
    z=v.Times(u);
    System.out.println("v * u: "+ z);

    z=u.DivideBy(v);
    System.out.println("u / v: " + z);
    z=v.DivideBy(u);
    System.out.println("v / u: " + z);

  }
  
}

Polymorphism

 
  public Complex Times (double x) {

    return new Complex(u*x, v*x);
    
  }

class RealComplex  {

  public static void main (String args[]) {
  
    Complex v, z;
    double x = 5.1;


    v = new Complex(3,-4.5);
    System.out.println("v: " + v);
    System.out.println("x: " + x);


    z=v.Times(x);
    System.out.println("v * x: " + z);


  }
  
}

In some object-oriented languages like C++ you can not only overload methods but even operators like + and =. However while this makes numeric classes like complex numbers easier to work with, it tends to lead to unreadable and unmaintainable code for non-numeric classes. Therefore Java's designers elected not to add this feature to the language. As you can see from our example, with a little forethought you really don't lose very much without operator overloading.

Exercises

1. Add a method to the Complex class that adds a real number to a complex number and returns a complex number.
2. Add methods for subtracting a real number from a complex number and for subtracting a complex number from a real. Be careful since subtraction, unlike addition, is not commutative.
3. Add methods for dividing a real by a complex number and for dividing a complex number by a real. Be careful since division, unlike multiplication, is not commutative.

Scope: Calling the Complex Class From External Classes

There has been some code that hasn't resided in our source files. Remember all those import statements at the top of every file? What they do is pull in prewritten and precompiled code from various locations so we can use it in our programs. You can do the same thing with classes you write. However to do this you do need to be aware of several conventions and restrictions.

1. No file should contain more than one public class. This means that our Hello World, Goodbye World example is no longer valid because each of the classes was public.
2. All files should have the same name as their single public class followed by the extension ".java".
3. Source code files should be stored in the same directory as their compiled .class file. This is so the Java compiler can find the appropriate definitions and interfaces for a class when the class is referred to in a different file.
4. Source code and .class files should be in a directory that's part of the $CLASSPATH environment variable.

Next save the examples from the previous exercises in a separate file called ComplexExamples.java in the same directory as Complex.java. Now compile both files and run Complex Examples.java.

The Mandelbrot Set

Here and in the future we are going to try to separate the mathematical definition of our data from its display on the screen. In fact we won't even add the screen display till the second iteration of the program.

Our data structure will be a two dimensional array, each element of which represents a fixed point in the complex plane. The array is defined by the value of the lower left point, the gap between points and the number of pixels in the x and y directions. Thus given that element (0,0) of the array matches the complex point (x0,y0), each point is separated by a value gap, we know that element i,j of the array represents the point (x0 + i*gap, y0 + j*gap) in the complex plane. Since we know this by position of the array element alone we dont' need to store this value in the array.

What will we store in each element of this array? We'll calculate a number to go there in the following fashion. Let z = 0 + 0i and let c be the position of that array element in complex space. calculate z = z*z + c and iterate as follows up to 200 times:

for (i=0; i < 200; i++)  {
  z = z.Times(z) + c;
}

Unfortunately there's no guarantee that just because an element doesn't reach 2 in two hundred iterations it might not reach two on the two hundredth and first iteration or the two thousandth or the two millionth. However most numbers that don't prove they're not in the Mandelbrot Set by the two hundredth iteration are reasonably likely to be in it.

Here's how the code will work. First we'll select the lower left hand corner of our rectangle in complex space, the size of the gap between the points and the number of points in each dimension. For a specific example we can choose the square bordered on the lower left by (-2,-2) and on the upper right by (2,2). To keep initial computations manageable we'll break this up into an array of 101 by 101 elements which implies a gap size of 0.05.

Once this array is created we'll loop through it and fill each element with a Boolean value, true if the element is probably in the Mandelbrot Set (doesn't pass two in two hundred iterations) and false if it's not (does pass two and thus go to infinity). Here's the code:

class MandelApp {

  public static void main(String args[]) {

    int xdim = 101;
    int ydim = 101;
    double xstart = -2.0;
    double ystart = -2.0;
    boolean Mandel[][] = new boolean[xdim][ydim];
    double gap = 0.05;
    int max_iterations = 200;
    int i,j,k;
    Complex z, c;

    for (i=0; i < xdim; i++) {
      for (j=0; j < ydim; j++) {

        c = new Complex(xstart + i*gap ,ystart + j*gap);
        z = new Complex(0.0, 0.0);
        k=0;
        while (z.Magnitude() < 2.0 && k < max_iterations) {
          z = z.Times(z);
          z = z.Plus(c);
          k++;
        }
        if (z.Magnitude() < 2.0) {
          Mandel[i][j] = true;
        }
        else Mandel[i][j] = false;
      }
    }
  
  }
}

Drawing the Mandelbrot Set

import java.applet.Applet;
import java.awt.*;

public class Mandelbrot extends Applet {

  int xdim;
  int ydim;
  double xstart = -2.0;
  double ystart = -1.25;
  int Mandel[][];
  double gap = 0.05;
  int max_iterations = 256;

  
  public void paint(Graphics g) {
  
    int i,j,k;
    Complex z, c;
    
    xdim = size().width;
    ydim = size().height;
    gap = 2.5/ydim;
    Mandel = new int[xdim][ydim];
    
    for (i=0; i < xdim; i++) {
      for (j=0; j < ydim; j++) {
        c = new Complex(xstart + i*gap, ystart + j*gap);
        z = new Complex(0.0, 0.0);
        for (k = 0; z.Magnitude() < 2.0 && k < max_iterations; k++) {
          z = z.Times(z);
          z = z.Plus(c);
        }
        g.setColor(selectColor(k));
        g.fillRect(i, j, 1, 1);
      }
    }
  
  
  }
  
  
  protected Color selectColor (int num_iterations) {
  
    if (num_iterations > max_iterations) return Color.black;
    else if (num_iterations > 9*max_iterations/10) return Color.darkGray;
    else if (num_iterations > 8*max_iterations/10) return Color.gray;
    else if (num_iterations > 7*max_iterations/10) return Color.magenta;
    else if (num_iterations > 6*max_iterations/10) return Color.cyan;
    else if (num_iterations > 5*max_iterations/10) return Color.blue;
    else if (num_iterations > 4*max_iterations/10) return Color.green;
    else if (num_iterations > 3*max_iterations/10) return Color.yellow;
    else if (num_iterations > 2*max_iterations/10) return Color.orange;
    else if (num_iterations > 1*max_iterations/10) return Color.red;
    else return Color.white;
  
  }

}

For more details on the Mandelbrot Set see the first chapter of A.K. Dewdney's The Armchair Universe.

Exercises

1. Explore different starting points and gap sizes for the Mandelbrot set. To make this easier add user input to dynamically select the starting point and gap size.
2. What happens if you allow the x and y gap size to be chosen independently?

Acknowledgements

The presentations at the first Java Day in New York City were crucial to getting my understanding of Java off the ground, especially those of Bill Joy and Frank Greco.

The eventtutor applet, flying lines applet and Mondrian applets are taken in spirit if not in code from Dave Mark and Cartwright Reed's Macintosh Programming Primer.

Finally I'd like to thank Olivia Whiteman, Dave Fisco, Tim Arnold and all the other Java Invaders for putting together forums in which I could learn more Java.