The Fractal Dimension of ZIP Codes
One quick way to look at ZIP codes is by seeing how each part of a ZIP code defines a part of our country. Ben Fry, of Fathom, created a simple visualization called zipdecode to do just this. As you type each successive digit of a ZIP code and see what regions of the United States it describes. For example, if you’re typing in 64110 (Kansas City), you can see what parts of the United States begin with ‘6’.
But let’s think about ZIP codes a bit more abstractly. ZIP codes must serve every resident of the United States in an efficient manner, much like how the circulatory system serves every cell within an animal. Circulatory systems, however, all have a certain shape: they are self-similar. Parts of these branching circulatory systems look like the whole.
And it turns out that branching structures, whether circulatory systems or not, are fractals. Essentially, that means that that they have fractal (or fractional) dimensions, since they fill space or a surface, but are built up using lines. The circulatory system fills a three-dimensional space using tubes (which are essentially two-dimensional), and the Peano Curve fills a plane while only being a long and snaking one-dimensional line. These objects, that don’t quite obey regular shapes, all have fractal dimensions.
» via Wired
(via clearwithsparkles)
