Fractal Generators

I've made two versions, an experimental JavaScript version using HTML5 (canvas and web workers) and an older one in Java (applet and .jar). The Java version is much more full featured at the moment. If you want to export high-rez images, download the .jar file to run the standalone Java version.

Controls for the Java applet:

Zoom: mouse scrollwheel
Moving: click and drag or arrow keys
Change Detail: +/- keys increase and decrease detail

The non-applet version (download the .jar) also has two more options: an Export menu which allows high-quality PNGs to be produced, and a re-sizable window.

The JavaScript version has a cut-down version of the same controls - drag the mouse to move and use the scroll wheel to zoom. Detail should automatically adjust itself.

Maths

I won't explain all the maths behind this here, others have already done this far better than I could. The Wikipedia page on the Mandelbrot set is a good place to start, it details the algorithm quite well. Unfortunately wiki's Julia sets page is almost incomprehensible; fortunatly I found this page which describes both the algorithm behind calculating the Julia set and a good method of colouring them. I found a good way of smoothing the bands of colour from here.