What are Fractals?

The word fractal is derived from the latin "fractus" meaning broken. It was first used by the mathematician Benoit Mandelbrot to describe objects too irregular to be described by classical geometry.

In general Fractals are sets of numbers that form shapes or objects that have the following properties:

1. Fine structure
2. Self-similarity
3. A relatively simple definition, usually involving recursion
4. Irregularity, they are difficult to describe using traditional geometry
5. A fractal dimension that is greater than the topological dimension

You can find some more detailed definitions for fractals at these sites:

Wolfram MathWorld

Wikipedia

If you're interested in the algorithm for how these Julia and Mandelbrot set fractals are made, I added a page covering the basics:

How To Make Julia And Mandelbrot Set Fractals