Jim has a unit square.
- On top of this unit square, he places a square with side length equal to \(\frac13\) the side length of the square below.
- On top of that square, he places another square which again has side length equal to \(\frac13\) the side length of the square below, and so on.
- He repeats this process until he has created an infinite stack of diminishing squares--a fractal.
What is the ratio of the perimeter of the fractal to the area of the fractal?