Example

An example of a self-similar object is the Sierpenski triangle show below.

As one looks closer we observe that the large triangle is composed of three smaller triangles galf the size of the original, which in turn are composed of three smaller triangles, and so on, and so on. On all scales the Sierpenski triangle is an exactly self- similar object.

An interesting way to think about fractals is that they are structures that grow from replicating the shape of a single seed. This replication is called recursion. Each phase of recursion is called an iteration. The diagram below shows the recursion of a single seed shape through 4 iterations.