A Portrait of the City as a Squiggly Line

This is very much à propos of none of the grand debates about the future.  It can hardly be, because urban form is necessarily so static, so hard to change, so grounded in heavy expensive physical bricks.  It's something we're pretty much stuck with whatever else happens.

A recent post on transit consultant Jarrett Walker's blog Human Transit discusses why it's misleading to talk about the average density of a city or urban area.  There are other factors, but mainly it's misleading because the average tells us nothing about the shape of the curve, and also because it averages over land area when, in trying to decide policy, we ought to think about what affects the most people.

The US Census Bureau defines urban areas by taking a city center and eating up adjacent blocks until it reaches areas that are not built up (or another urban area.)  The blocks that are included are contiguous blocks with density at least 1000/sq. mi. and adjacent blocks with density at least 500/sq. mi.  Such an area will include both high-rises and suburbia, and the average density (which the Census Bureau provides) tells us nothing about urban form.  For example, it rates Los Angeles as more dense than New York, which is obviously misleading.  Nevertheless, as we shall see, our prejudices are also often misleading, and more detailed and meaningful numbers can help us adjudicate between the two.  So I downloaded some data from the 2000 census and made the following graphs, whose x-scale is pleasingly logarithmic:

The first shows the percentage of people within the urban area who live in a block group of a higher density than the x coordinate; the second shows the total number of people who live in block groups with density x±5%. I included six cities I've either lived in or visited since I started thinking about urban form, as well as two others (Las Vegas and Atlanta) purely for comparison.  I used Census-defined urban areas except for the Bay Area, which combines the Census's San Francisco, San Jose and San Rafael (Marin County) areas.

There are a number of things that stand out in this graph, both obvious and surprising.  Without much prejudice as to which is which, here are some of them.
  • The densities of older cities (New York City, Chicago, and Boston) are essentially bimodal, with a dense, older urban core surrounded by low-density suburbs built up after World War II, although Boston's curve is oddly flat.  The densities of newer cities are essentially unimodal.  Everyone in LA lives at broadly the same density -- it's no accident even Italo Calvino called it a city without form.
  • About 7 of the 18 million people in greater New York City -- the vast majority of whom form much of the population of the city proper -- live at densities that are home to only about 5% of LA, the Bay Area, Boston and Chicago.
  • On the other hand, LA's curve is pretty much uniformly higher than Chicago's; for any given density, there are more Angelenos living above it than Chicagoans.  This is worth dwelling on because most people think of Chicago, and not LA, as a Real City with tall buildings.  I suspect I know the reason for this.  The densest parts of Chicago are the Loop and the lakeshore on the North Side; these are also the most affluent, most-visited, most touristy parts.  On the other hand, the touristy, impressive, upscale parts of LA are spread all over the place, and are mostly not in the densest parts, which are the areas just east and west of Downtown as well as South Central, that place whose condition is so shameful they gave up and renamed it to South LA.  (Hollywood is also very dense, but, outside the famous bits, also rather poor.)  Even if you live in a city, you are mostly a tourist outside your own neighborhood, and so the parts you see are unrepresentative.  "[Y]our stereotype of Los Angeles may be a ranch-style house with a big pool on a cul-de-sac," writes Jarrett; indeed, we think of LA as low density because when we think of a city we first think of its sparkly rich parts.  (I kind of exclude myself from this 'we' since I like to grub around in ethnic neighborhoods, but it still applies to some degree.)

    This also makes me suspect that the best public transit model for LA would be the one that Chicago uses: rail lines that go to most places, but not necessarily from everywhere to everywhere, and faster, better buses.  This seems to be what is already happening, but it will require free transfers and higher frequencies off-peak to make it really convenient.
  • While the most common density for the other Western cities is between the two peaks of the Eastern ones, Seattle, despite its hipster image, seems to pretty much be a sea of sprawl; it has a single peak which is around that of New York and Chicago's suburbs.
  • Atlanta deserves its reputation as a sprawl capital.  Not only does it entirely consist of low-density suburbs, but those suburbs are actually considerably lower-density than those of other cities.
  • Las Vegas is middling dense, if you average over the metro area, but amazingly uniform.  Half its population lives in densities within a factor of two of each other.
Of course, you can't glean everything about an urban area's character from this graph.  There's a lot to urban growth patterns that you can't quantify even locally with a single number; Jarrett speaks eloquently about this, so I won't try.  But having numerical data that does say something helps us think through our misconceptions and make arguments that aren't just based on hunches and case studies.

I'd be curious to try this on cities outside the United States, and on more diverse urban forms, but not so curious as to look for the data myself.


  1. Neat. I'd be very interested to see Washington, DC and Baltimore to the graphs.

  2. Hello, I really like these charts and would be interested in trying to recreate them for English cities. How did you produce them?

  3. I wrote a python script to hack apart census data; the code is living here for now. I'm really curious to see non-US cities as well. I tried briefly, but it seems that other countries don't make their census data as accessible as the US does.

  4. Thanks. The English census data is indeed quite tricky to either find or understand, but I'm working through it at the moment. If I get anywhere with it I might get back to you, as Python is a bit of mystery to me!

  5. I made a graph including London with some larger US urban areas. London data is old, from 2001, but that's what I found. Used the US Census 2010 data. I graphed both Greater London and the London Larger Urban Zone, as defined by the EU, which may be equivalent to an American metro. The census units I used for London are LSOAs, which contain roughly 1500 people each. Their boundaries are drawn differently than American ones, with American ones tending to avoid mixing residential and non-residential blocks together while British ones mix them more. So the lower density LSOA may be underestimated. In particular, some of the lower density tail London Urban Zone looks too low; the exurbs of London should be similar to Los Angeles, not less dense than NYC. The denser part of the London curves should be about accurate.