I’ve been interested in the Mandelbrot Set since I first saw it described in Scientific American sometime in 1989 (as best I recall). But my first efforts with it soon revealed that access to a high-speed computer, especially one with a lightning-fast floating-point calculator, was essential to its satisfactory investigation. In those days people commandeered the so-called “supercomputers” to generate Mandelbrot views. A home machine could take hours per image, even with low resolution and a shallow calculation depth.
Now at last the single processor in a personal computer has reached adequate speed. You still can’t swoop down into an evolving spiral as a hawk dives on a dove, but you can examine one deeply by tolerating small delays, about at the rate of a botanist studying flower stamens with magnifier and microscope. You no longer have to wait minutes for the next view to appear. Now they paint in seconds — if the speed of your machine is 500 MHz or better. I refer to high-resolution views, 1024x768 or better, with a reasonable calculation depth of 2048 iterations and that many colors, maximum per pixel.
I herewith offer two programs as freeware, no string attached. The first is intended for unrestricted exploration to a maximum magnification greater than 10^13 (ten trillion to Americans), compared to the top view of the set, which I call Mag 1. To give you the idea, if the full set on a 15" monitor is ten inches tall, such magnification produces a Mandelbrot Set 1.57 billion miles tall. For comparison the average diameter of the planet Saturn’s orbit is 1.78 billion miles.
The second program is a screensaver that runs around the rim of the Mandelbrot Set at a fixed magnification of 300. On a 500 MHz machine it requires about ten hours to complete the positive half of the set. It has been updated to run under Windows-XP.
Both programs run only under Windows 95, 98, ME, XP (Home) and NT. They will most likely work fine under Windows 2000 and XP Pro, but I have not tested them on those systems.
Installing the first program, mandex.exe, is a cinch. Just download it into your choice of folder and drag out its shortcut to your desktop, where it shows an icon that somewhat resembles a Mandelbrot top view. It requires nothing in the Windows Registry, so uninstalling it is also a cinch: just delete it from your hard drive. Double-click on the icon to invoke it. It starts out by taking over your screen and painting the top view at Mag 1, then displaying an information box with the commands it recognizes. Their use should be pretty obvious. I didn’t put them on a menu bar because I wanted to leave the maximum space available on your screen to hold the generated image. You can also invoke mandex via a DOS window or by dragging to the icon one of the files it or the screensaver has previously saved, a file with extension .MCO, which contains the coordinates of a view.
mandex can also output its views as Microsoft bitmap files (*.BMP). In the S command dialog box pull down Save as Type: to Bitmap File. Unlike the tiny coordinate files, bitmap files are huge, approaching three megabytes, depending on the pixel dimensions of your display screen, but many programs exist that will compress bitmap files to less than 200K bytes in the JPEG format.
Installing the second program, mandelrimmer.scr, is a bit more involved. After downloading you must move or copy it into the folder, c:\windows\system32 After that, click on Start: Settings: Control Panel: Display: Screensavers and select mandelrimmer as your screensaver. The initial screensaver display is necessarily drawn by individual pixel calculations as if under mandex, but once the initial display, a view of the butt crack, is onscreen it begins to move up and to the right, picking up speed as it leaves the black, where the calculation is slower. If you interrupt it by moving the mouse or pressing a key, as usual for terminating a screensaver, the program saves the current display coordinates in a file called mandplac.mco, located in the top folder of your C: drive, from which you can retrieve them with mandex if you wish to explore that area more deeply.
When the screensaver has proceeded completely around the positive (upper) half of the set and reached the long drawn-out left end, it starts over in the butt crack.
Windows XP appears to want its screensavers’ names to begin with “ss.” If you are installing under Windows XP, after downloading or moving the SCR file to c:\windows\system32, change its name (select the name under Windows Explorer and strike F2) by prefixing the two letters, ss, so that it becomes ssmandelrimmer.scr. It may work better.
Uninstalling the screensaver requires choosing None or some other screensaver, then deleting the file from c:\windows\system32. You may have to restart your machine before Windows will let you delete it.
Note that I, Kellis, am the author of both these programs. They were written entirely in C and Assembler using a version of the Microsoft Visual-C SDK and are entirely original save for the Microsoft-furnished library calls. I hereby place them in the public domain.
Some will ask why I publish them here, in a web page devoted to analysis of the human propensity toward sexual behavior. To me sex has always represented a kind of visceral beauty. Just as flowers, the sex organs of plants, are unanimously acclaimed as representatives of beauty, so too in my opinion are those characteristics, both of appearance and behavior, in the human female that recommend her to the male — and vice-versa. Judging by the popularity of this web page in particular and the sex newsgroups in general, others must share this view. How else to explain their fascination with what amounts to irregular pressures among electrons on a wire?
The wild detail, often sinister, more often breathtaking, along the rim of the Mandelbrot Set, its infinite and awesome complexity arising from such a simple program loop, is the same kind of beauty.
Note: An MCO file contains only the coordinates of a view, expressed in ASCII decimal and typically less than 100 bytes long. It makes a great, low-bandwidth attachment to Email. I’d love to see what you think is pretty. In exchange I’ll send you a representative of my opinion.