Just by making slight alterations to the formula you use, you can create loads of completely different pictures. Most of them are very boring but here are some of the really good ones.
In many cases I have forgotten exactly what I did, but you probably aren't bothered anyway.
The pic in at the top left and this one are (I think) very similar in thier creation. I think I just changed one value from two in a normal Mandelbrot to three here and nine in the top left pic. The ranges of both pics are -2..2 and -2..2i. This took 25 mins that one took 91 mins.
The pic on the left is very similar to the Mandelbrot set. It uses the same formula except that each iteration is raised to the power 4 instead of been squared. It's range is -2..2 and -2i..2i.
The pic above is a close up of the part of the pic on the left. It's range is -0.5004..-0.4928 and 0.4304i..0.4227i. It took 97 minutes to render.
This is far and away the strangest picture I have ever generated. It was created (I think) by altering Pythagoras' formula for finding the length of the sides on a right angled triangle. It uses this to check at each stage it the number has a modulus (distance from the origin) greater than 2. I changed one of the squares to a 4th power just to see what would happen and well...
This pic is very similar to the one above. It was created by replacing pythagoras' formula x^2 y^2=z^2, used to find the displacement of the point from the origin, by the similar formula x^4 y^4=z^4. This doesn't actually give the length but does still allow for some interesting pictures to be generated. This one is the region from -0.67 to -0.62 parallel to the real axis and 0.77i to 0.72i parallel to the imaginary axis. This picture took over eleven hours to render.