Fractal Arrow

Fractals are an interesting and beautiful piece of mathematics. There are many ways to create fractal shapes, but one common way is through an iterated function system (IFS). Loosely, an iterated function system on the plane is a series of contractive functions which map points on the plane. If we iterate just one contraction, this is not very interesting. In fact, Banach's fixed point theorem asserts that this will result in a single fixed point as we take the limit in the number of iterations of this contraction. However if we consider several contraction mappings with different fixed points, what we are left with is an interesting IFS that fractalizes the plane.

This print started off as a solid arrow with no holes. The top portion of the arrow is simply a four sided polygon. The base of the arrow was slightly more complicated, and involved taking the difference of a triangle with three circles to create a sort of hyperbolic triangle. This formed two separate shapes which were t