Conway's Life is storied as fuck. It's one of the easiest, earliest and gnarliest screensavers, for starters. If I recall correctly the parameters aren't messed with much but initial conditions matter a lot.
I used to have a screen saver (talkin' Win95 era) that was loosely based on Conway's life, but allowed for bilateral and radial symmetry as well as four different block designs - offensive, defensive, locomotive and photosynthetic. It was super-cool to let run for a day or two because you got rudimentary predator-prey relationships in not too many thousands of evolutionary cycles.