Wikapedia defines a fractal as -- In colloquial usage, a fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole". The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured".

The following picture show the pattern formed by the Mandelbrot series 

and an expanded section of that same pattern.

I have generated two files which will give you the ability to display a fractal image produced by a simple Mandelbrot series. You may explore the many intricacies of this image which is generated by a simple, 8 line algorithm. Any portion of the image may be expanded by factors up to about 100,000,000,000,000 times their size. Yet the resulting sub image may be as complex as the original.

Here is a link to the files - Updated 5/11/07 to Version 1.02

Microsoft, in their attempt to protect systems against unknown sources of code now blocks programs not know to them. This protection has changed. As of this writing, in order to have both the program and the help features work, you must first download the .zip file to your machine, Then right click on the .zip file and select properties. At the bottom of the properties window, click Unblock. Then say "OK" to exit the properties window and open the .zip file. On the "File" menu (top left) select "Expand All" and follow the instructions to place the files wherever you want them. You may then discard the zip file.

After you start the program, put the cursor anywhere on the puzzle,  press "F1", and go right to "How To -> View the image" for a quick introduction.

Note: Help now works with Vista. If you had Version 1.01, you may delete the old help file.

Navigate the screen with only the mouse. Left button click to move a point to the center or drag to make a box to expand an area. Right button drags up or down to zoom the current location or double click to get back to the starting point. And of course, there are undo and redo buttons if you make a mistake.

When you find an image that you like, be sure to add it to your favorite file.

The ability to print the image is not implemented yet, but you can copy the image to the clipboard and then paste it into your favorite graphics editor program to print or save as you wish.

Comments to Gary at


The algorithm:

You can find the mathematical description on the web. In plane English, this is how it works:

for each pixel location x, y (in floating point real numbers) do the following
    start out with x1, y1, x1s, y1s, and the color index all equal to zero.
    while the sum of the squares of x1 and y1 is less than 4 and 
                the color index is less than 254, do the following 5 steps
        y1s = y1 * y1             calculate y1 squared
        x1s = x1 * x1             calculate x1 squared
        y1 = y + 2 * x1 * y1   calculate the next value for y1
        x1 = x + x1s - y1s       calculate the next value for x1
        color = color + 1         advance to the next color

note: for the display we cycle through the same 14 colors


Image draw time is generally less than 1 second for a 480 x 640 image on an 800 MHz computer.

You can navigate the image using only the mouse.

You can name images you particularly like and save that information for later viewing.

Context sensitive help on all controls.

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