One of the neat things that a PC can do that's really difficult, if not impossible, to do any other way is generate graphical representations of fractal formulas. Just about the best progam out there for doing this is the freeware program Fractint, so named for its generation of FRACTal images using INTeger math. Here are a few fractal images I've captured and some links to other fractal resources.
Some very simple fractals made with fractint:
Natural fractals
On the campus of Vanderbilt University:
Around my home in the Woodlands:
Some links to other fractal goodies:
Infinite Fractal Loop hompage
Braingames Fractals and Fractal Art listings