Intro to a Mandelbrot Applet

An Introduction to a Mandelbrot Applet

You're just one link away from an applet that computes and displays the Mandelbrot set. What's the Mandelbrot set? Well, it is the set of points on the complex number plane for which, when the coordinates of the point are plugged into a little iterative formula, the value of the formula never goes above '4', no matter how many iterations are computed. Of course, we don't have time to wait for "no matter how many iterations", so we pick a number, the iteration limit, and only loop through the calculation that many times. An image of the result is rendered by coloring each point according to how many times the calculation loops before the value goes above 4 at that point. Any point whose calculation value is still <4 after reaching the iteration limit is deemed to be a member of the Mandelbrot set and is colored black.

The applet has a few features which are controlled through the mouse:

Clicking on the rendered image will recalculate it, but with an iteration limit that is 50% higher. Also, 50% more colors will be used, up to a maximum of 216 (the supposedly "web-safe" colors).
Dragging out a square and clicking in the square zooms in on the enclosed area. Clicking outside the square erases it, in case you didn't get it positioned where you wanted it.
Using the mouse menu button brings up a menu providing a way to back up to the previously displayed image (i.e., to zoom out) and to animate the color map in various ways in case you want to hypnotize yourself. [WARNING: Since developing this under Apple's Applet Runner, I've had the chance to test this on a few other platforms, and most of them didn't display the popup menu. Someday I hope to find time to work on this.]

Now you have two choices:

BIG (500 x 500)

LITTLE (200 x 200)

Choose BIG if you are patient and/or have a fast machine. For reference, the applet was developed on a 120MHz PowerMac 604 and I usually found it fast enough for the big size. (But then, I'm patient because I wrote the thing.) Ironically, I can't look at this with my own browser because the Java implementation in Macintosh Netscape 4.76 has a flaw that prevents it.

Something you might notice is that if you zoom in far enough, the picture gets distorted. This is because the area on the complex plane has become so small that even double precision numbers do not provide enough resolution to divide it up into the requisite number of pixels. The program doesn't check for this.