In mathematics, we are often interested in describing the characteristics of shapes – whether that be perimeter (length), area or volume.

In this task we will investigate some of these shape characteristics for a “mathematical snowflake”, defined using a recursive process (a process that repeats the same steps over and over again). A recursive process is often easy to carry out by hand for a few steps, but becomes very difficult for many steps. Recursive processes can create quite complex mathematical objects that we want to understand well. We study these recursively defined objects in two ways: (1) by using the computer to help us carry out many steps of the process, and (2) by noticing patterns in the process that we can take advantage of and use to study the object analytically.