Barnsley Fern is perhaps the most famous IFS fractal there is. It was named after the discoverer or IFS fractals, Michael Barnsley. It starts with a point and uses 4 transformations on a plane (see IFS iteration) to create the fractal:
Notice the self-similarity of this fractal. If you take any of the fernís leaves, you will see that they are identical in shape to the entire fern. Obviously, fractals such as this one are very useful in modeling plants.
NOTE: This is the fractal we used on our splash screen.