In a similar spirit, I decided to explore the dimension of the ZIP Code system and see if it has a similar type of fractal dimension. I did this using the wonderful images created by Robert Kosara calledZIPScribbles, which connect the coordinates of sequential ZIP codes (02445 is connected to 02446, 02446 is connected to 02447, and so forth). As you can see below, there is a geographically hierarchical nature to it. ZIP codes divide the population first into states, and then divide into little scribble regions even further, in a self-similar fashion.
So, I set out to measure the fractal nature of the ZIP code system. I used one of the simplest methods, called the box-counting method, which estimates the self-similarity of a shape by looking to see how many boxes in a series of ever-smaller grids are required to cover a shape. Doing this, I was able tocalculate the fractal dimension of the ZIP Code system, using the ZIPScribble: 1.78.
(via Wired: “The Fractal Dimension of ZIP Codes”)