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Explore the famous Mandelbrot set - Java training

by: fresherlab on Date: Sat, 31 Jul 2010 Time: 9:41 AM

Java Training
Sun Microsystems is a provider of network computing and infrastructure solutions. Some of Sun Microsystems well known brands include the Solaris operating system and the Java technology platform. Sun provide several certification exams to educate IT professionals on their products. Some Students with some exposure to Java training may wish to get certification for their skills and who may wish to further their career as a Java Programmer. There are many career benefits to becoming a sun certified java programmer. You have evidence that you are a Java programmer and have the proof, knowledge and skills to design and develop code based on J2EE. You will also gain more respect among your employers and associates as your job security and opportunities are improved. You also will become more competitive in the job market as the skills you have learned are in high demand.
The Mandelbrot set is a set of points in the xy-plane that is defined by a computational procedure. To use the program, all you really need to know is that the Mandelbrot set can be used to make some pretty pictures, but here are the mathematical details: Consider the point that has real-number coordinates (a,b) and apply the following computation:
Let x = a
Let y = b
Repeat:
Let newX = x*x - y*y + a
Let newY = 2*x*y + b
Let x = newX
Let y = newY
As the loop is repeated, the point (x,y) changes. The question is, does (x,y) grow without bound or is it trapped forever in a finite region of the plane? If (x,y) escapes to infinity (that is, grows without bound), then the starting point (a,b) is not in the Mandelbrot set. If (x,y) is trapped in a finite region, then (a,b) is in the Mandelbrot set. Now, it is known that if x2 + y2 ever becomes strictly greater than 4, then (x,y) will escape to infinity. If x2 + y2 ever becomes bigger than 4 in the above loop, we can end the loop and say that (a,b) is not in the Mandelbrot set. For a point (a,b) in the Mandelbrot set, this will never happen. When we do this on a computer, of course, we don't want to have a loop that runs forever, so we put a limit on the number of times that the loop is executed:
x = a;
y = b;
count = 0;
while ( x*x + y*y < 4.1 ) {
count++;
if (count > maxIterations)
break;
double newX = x*x - y*y + a;
double newY = 2*x*y + b;
x = newY;
y = newY;
}
After this loop ends, if count is less than or equal to maxIterations, we can say that (a,b) is not in the Mandelbrot set. If count is greater than maxIterations, then (a,b) might or might not be in the Mandelbrot set (but the larger maxIterations is, the more likely that (a,b) is actually in the set).
To make a picture from this procedure, use a rectangular grid of pixels to represent some rectangle in the plane. Each pixel corresponds to some real number coordinates (a,b). (Use the coordinates of the center of the pixel.) Run the above loop for each pixel. If the count goes past maxIterations, color the pixel black; this is a point that is possibly in the Mandelbrot set. Otherwise, base the color of the pixel on the value of count after the loop ends, using different colors for different counts. In some sense, the higher the count, the closer the point is to the Mandelbrot set, so the colors give some information about points outside the set and about the shape of the set. However, it's important to understand that the colors are arbitrary and that colored points are not in the set. Here is a picture that was produced by the Mandelbrot Viewer program using this computation. The black region is the Mandelbrot set:

When you use the program, you can "zoom in" on small regions of the plane. To do so, just drag the mouse on the picture. This will draw a rectangle around part of the picture. When you release the mouse, the part of the picture inside the rectangle will be zoomed to fill the entire display. If you simply click a point in the picture, you will zoom in on the point where you click by a magnification factor of two. (Shift-click or use the right mouse button to zoom out instead of zooming in.) The interesting points are along the boundary of the Mandelbrot set. In fact, the boundary is infinitely complex. (Note that if you zoom in too far, you will exceed the capabilities of the double data type; nothing is done in the program to prevent this.)
Use the "MaxIterations" menu to increase the maximum number of iterations in the loop. Remember that black pixels might or might not be in the set; when you increase "MaxIterations," you might find that a black region becomes filled with color. The "Palette" menu determines the set of colors that are used. Different palettes give very different visualizations of the set. The "PaletteLength" menu determines how many different colors are used. In the default setting, a different color is used for each possible value of count in the algorithm. Sometimes, you can get a much better picture by using a different number of colors. If the palette length is less than maxIterations, the palette is repeated to cover all the possible values of count; if the palette length is greater than maxIterations, only part of of the palette will be used. (If the picture is of an almost uniform color, try decreasing the palette length, since that makes the color vary more quickly as count changes. If you see what look like randomly colored dots instead of bands of color, try increasing the palette length.)
If you run the Mandelbrot Viewer program as a stand-alone application, it will have a "File" menu that can be used to save the picture as a PNG image file. You can also save a "param" file which simply saves the settings that produced the current picture. A param file can be read back into the program using the "Open" command.
The Mandelbrot set is named after Benoit Mandelbrot, who was the first person to note the incredible complexity of the set. It is astonishing that such complexity and beauty can arise out of such a simple algorithm.

About the Author

Fresherlab.com is a young organization, based at India’s IT hub, Bangalore.
It's a dynamic and competitive world with full of ups and downs in IT sector and therefore; the fresh engineers require just more than theoretical knowledge to get themselves ready for the industry. Academic institutions across the world provide the basic and conceptual fundamentals covering multiple areas in computer science. With increasing number of graduating engineers, but with constant number of companies, it becomes difficult for fresh engineers to compete with their unpolished skills because they need more effective and specialized quality training.

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