Just recently I put the finishing touches on a little program that generates images of fractals. Despite the fact that it's really slow and probably doesn't do as much as a lot of other fractal programs out there, you can download it if you want to. I also have some nifty images that were made by it that I can share. If you click on any of the tiny versions you'll get a big 1600x1200 version that you can download and use as a background. I might get some other sizes up eventually, too.


This is a picture of the Mandelbrot set. It serves as an index to the Julia sets: the points on the inside of the set (marked in black in this rendering of it) correspond to connected Julia sets, and the ones on the outside correspond to disconnected ones.


One of the interesting things about fractals is that they are infinitely complex: you won't find a single bit of unimpeded straight line along the edge of the Mandelbrot set, and the set contains infinitely many tiny copies of itself. This image here is a close-up of a small section near the top of the first.


This is the Julia set corresponding to the point (-1.1175, 0.2575) on the Mandelbrot set. Since that point is near the edge of the Mandelbrot set, it is connected, but just barely. This category of Julia set tends to be the most interesting-looking.


Another Julia set, this one corresponding to the point (-.485352, -.600586).


All these sets are generated by an algorithm that involves squaring a complex number repeatedly. In the fractal program, though, you can change that exponent from 2 to something else. Here's a Julia set generated by the point (-.762451, .884033) with an exponent of 5.


This is a side-by-side comparison of a close-up of an area just off the edge of the Mandelbrot set, centered on the point (.380117, .285898) and the Julia set corresponding to that same point. Note the similarity between the forms displayed in both images.