The Mandelbrot Set

The Mandelbrot set is a mathematical object like a line or a circle, but much more complex.

It can be visualized using pictures like this graphic of a portion of the set:

The Mandelbrot set is a type of fractal. Like many fractals, it has an infinite amount of detail. You can zoom in closer and closer and seem more detail that never repeats or runs out.

I’ve written a simple program for viewing the Mandelbrot set. To download it, click here. It’s only 88 Kb. The program can be used to make movies like these:

Endless Spiral (11 Mb, Windows Media)

Panning Around (23 Mb, Windows Media)

The movies are rather large and require a fast connection.

Below are some simple instructions for using the program. The program has an extremely crude interface and violates many interface guidelines.

The first time you run it, the program starts up showing the entire Mandelbrot set. You can navigate around the set by:

            Zooming

To zoom, use the mouse to drag a rectangle around the part of the image you want to focus on

            Centering

Double click to center the image on a point

            Go back

Hit the backspace key to go to the previous image

            Go home

Hit the period key (“.”) to go back to the home image

File Save

Saves the current image to c:\dib.bmp. Yeah, that’s lame.

Options Adjust

Brings up tuning options. The only really useful options is “Maximum Iterations”. This controls the maximum number of steps taken to color each pixel. Increasing this value brings detail into more of the black areas but makes the image draw more slowly.

Many of the other options are used for making movies. This page doesn’t describe movie making.

If you zoom in closer and closer then eventually the image will degrade into horizontal lines or a solid color. This is due to the limited precision of the 64 bit floating point numbers used inside the CPU. Other Mandelbrot programs available on the web use infinite precision and can zoom in much further.