When studying fractal geometry, we might iterate a function that maps sets to other sets. Such an example is shown in Figure 5. The limiting figure, called the Sierpinski triangle is shown in Figure 6.

The specific type of function that we iterate in this context is called an iterated function system Some amazingly intricate images can be constructed using an iterated function system. Figure 7 shows the Barnsely fern, which is described by a list of just four functions.