Density Profiles of Cities

 Playing around with my WeAloneOnEarth code, testing it against cities* I've lived in, started getting some interesting results:

Suggesting Phoenix is more like Salt Lake than Raleigh is counter-intuitive: aren't both Raleigh and Phoenix both sprawling sunbelt cities? Adding more cities makes it stranger:

Suggests that in some fundamental way, a surprising array of cities in the west are similar, and very different from places in the sprawling south. Adding more major southern cities only reinforces things:

Compare and contrast on some extreme cases is interesting: LA is its own thing, as different from Phoenix as Phoenix is from Atlanta.  

But all show a distinct 'peak' showing their median density, which is radically different from Boston or NYC.

Seems worthwhile to parameterize the logistic-style curves in the first chart. The result is a pretty good fit, with the interesting implication that NYC is in fact lacking in high density development, and there are a lot of tracts near 10^4 when they should be nearer 10^5. 

Altogether, these two charts together suggest that we can describe every city in American using two numbers: a median population, and a k-value. Hypothetically, Cleveland would probably have a peak at 10^.37, with a K value of 3.5. In actuality, Cleveland peaks (minimally), but has a much higher K value than expected (k=4.79) such that it is much more like Atlanta(!) than Chicago and seems to be missing high-density tracts in the 10^(3.5-4) order of magnitude. 

Next step may be to map this - if I was to arbitrarily declare 10^3 (1000 persons**/square kilometer) to be transit suitable densities, what would each of these cities look like, and how would that align to their transit networks.

#--------------------------------------------------------------------------------------------------------------------

*The term city is used casually here; the data is for census urbanized areas. A city as a legal and territorial jurisdiction isn't relevant in this context. 

**At some point I'll need to include employment into these estimates--employment concentration is critical for effective fixed guideway transit, probably more important than population density.