Hope you enjoy the site. I've been interested in the Mandelbrot set since 1986, when I read the Scientific American article on it. At the time I was in high-school, and I had a PC. I remember creating a simple BASIC program to plot the Mandelbrot set based on the information in the Scientific American article. It took the computer all night to render a tiny 256x256 pixel image. In those days you had to be a bit of a freak to look at fractal imagery because it often took many hours, days or weeks for the computer to create a single image.
As the years went by PCs got faster, until today your average gigahertz class PC can render large images in a few minutes or less.
Not only did I create these web pages, but I also wrote the program which created all the images. Now it's not very hard to write a program to look at the Mandelbrot fractal. The heart of the program is a very simple feedback loop. Almost all programs out there use the PCs builtin floating point arithmetic when calculating the fractal. This is good because todays PCs have very fast floating point (real number approximation). However, this is bad because it limits how far one can zoom into the fractal before exhausting the precision of the floating point arithmetic.
Assume your zoom window is 12" square, 1000x1000 pixels. Each subsequent factor of two zoom doubles the 'top level' image size. Programs that use the PC's floating point arithmetic allow one to zoom in so far that the 'top level' Mandelbrot shape (which again was 12" square on the first zoom) would stretch from the Sun to the orbit of Jupiter or so. That's a lot of real estate.
The program I wrote does not use the PCs floating point math. I created my own arithmetic routines using fixed point numbers. My program increases the precision of the arithmetic as needed, until its precision is exhausted (256 bits). With the program I wrote one can zoom in so far the top level Mandelbrot set would exceed the size of the known universe (whatever 2^230 feet is). Since my program never uses the computers floating point arithmetic, and it only allows power of two zooms, I can exactly track how far I've zoomed into a given point.
Even this isn't anything new, as there are several programs out there which already have deepzooming capability. However computers haven't gotten fast enough until recently to make this practical. My program is much slower than an equivalent one using floating point math, but I think it yields a better result, and it allows one to zoom into the fractal much further (see the zoom sequences in the mandelbrot tutorial). I had to wait over a week for some of the poster sized images in the gallery to be created.
Many of the images in the gallery are taken from tiny windows into spaces billions of lightyears across.
The Mandelbrot set, a lesson in connectedness. A true Goddess, but not a human hearted one:
-Eric Bazan
