English: Barnsley's fern illustrates the use of affine translations in an iterated function system (IFS) to create a fractal. The small blue triangle of one half of one "leaflet" is transformed to the large red triangle of one half of one "leaf" or "frond". The "Collage Theorem" provides the other three transformations. The "stem" of the fern image is the first part of the fractal that is quickly completed after only a few iterations. It is an image of the whole set under one of the transformations. This image shows four separate states of the fractal during the course of iterations over time, plotted with VisSim..