On top is a clockwise rotation by 90°. It has order 4, because that is the smallest positive exponent that produces the identity. Below is a shear mapping with infinite order.
Below that are their compositions, which both have order 3.
In mathematics, an iterated function is a function that is obtained by composing another function with itself two or several times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying a given function is fed again into the function as input, and this process is repeated.
For example, on the image on the right:
Iterated functions are studied in computer science, fractals, dynamical systems, mathematics and renormalization group physics.