We've constructed three example programs in Java so you can get the feel of what fractals are like and do a bit of exploring. One program called Henon shows a lot about how attractors generate orbits [sets of points that appear during iteration and trap the calculation to run only within that set and produce no points outside the set]. Another grows a coral-like structure from a single origin. This uses the SloGro algorithm.

By far the most exciting of the examples is the Mandelbrot Explorer which lets you explore through the Mandelbrot set in real-time. You can pan and zoom to see unbelievable detail.