Alexander’s Distribution of Towns

In a recent post, I analyzed what it would look like to apply the first pattern of Christopher Alexander‘s A Pattern Language to North America. This pattern, titled Independent Regions, created 50 new, small nations or regions within what is today the United States and Canada. The next thing I wanted to try was applying Alexander’s second pattern, The Distribution of Towns, to one of those new regions. The pattern reads:

If the population of a region is weighted too far toward small villages, modern civilization can never emerge; but if the population is weighted too far toward big cities, the earth will go to ruin because the population isn’t where it needs to be, to take care of it.


Encourage a birth and death process for towns within the region, which gradually has these effects:
1. The population is evenly distributed in terms of different sizes- example, one town with 1,000,000 people, 10 towns with 100,000 people each, 100 towns with 10,000 people each, and 1000 towns with 1000 people each.
2. These towns are distributed in space in such a way that within each size category the towns are homogeneously distributed all across the region.

This process can be implemented by regional zoning policies, land grants, and incentives which encourage industries to locate according to the dictates of the distribution.

apl2diagramtowns of 1,000,000 – 250 miles apart
towns of 100,000 – 80 miles apart
towns of 10,000 – 25 miles apart
towns of 1,000 – 8 miles apart

However, as discussed in the previous post, not all regions that meet Alexander’s population criteria automatically meet his spacing criteria when you move from Pattern 1 to Pattern 2. Several regions are too large and sparse, while several more are too small and dense.

Click to enlarge.

Click to enlarge.

So to analyze Pattern 2 without worrying about redistributing the population of the regions until they were the right size, I wanted to pick one of the “Goldilocks” regions that is already about the right size. I went with the Washington DC Region.

Click to enlarge.

Click to enlarge.

Now for the distribution part. Let’s say that we have a region, Region A, with capital city City 1 in its center.Diagram1-01Alexander recommends one very large city per region, so we’ll assume that City 1 has a population of about a million and that it’s the only city of it’s scale in the region. Our first step is to identify our cities of 100,000 people. While Alexander recommended making these cities 80 miles apart, I used 72 miles to simplify the math a little bit. So we want to make sure that these cities of 100,000 are 72 miles from City 1, as well as from each other.Diagram2-01Next we want to identify our towns of 10,000. Again, I fudged Alexander’s math a bit, and identified towns that are 24 miles (1/3 of 72) from any larger cities or from each other.Diagram3-01And finally, we want to identify towns of 1,000 people, eight miles from any larger town and from each other.Diagram4-01That’s what it looks like in an ideal world. However, in the real world, we’re not starting with a blank slate, and rather than founding new cities that are perfectly spaced from DC, I wanted to identify existing cities located in the right place. When you do that, it looks like this:

Click to enlarge.

Click to enlarge.

What this technique doesn’t consider, however, is why cities are located where they are: largely, access to resources, and access to transportation. They aren’t distributed evenly across a landscape; they’re bunched up in the places that have access to mineral, agricultural or intellectual wealth, and places that have access to ports, railroads, and highways. Disregarding this truth about cities means that some cities that are not located the right distance away from one another can get hosed. Case in point, Richmond, a city of over 200,000 people at the center of a metro area with over 1.2 million, because it isn’t spaced correctly relative to DC, is relegated to the 10,000 people tier, meaning that a huge population would be resettled to areas like Tappahannock (current population 2,397) or Powhatan (current population 49) which are spaced correctly.

Also, by using Alexander’s spacing suggestions, one does not arrive at his suggestion for how many towns there should be. Based on this distribution, you end up with one town of 1,000,000, eight towns of 100,000, 45 towns of 10,000, and 319 towns of 1,000. That adds up to 2,569,000 people. But in the last pattern, we determined that the Washington DC Region would have a population of 8,917,843. So where are the other 6 million plus people living?

The answer to that actually comes from another pattern, number 5 in Alexander’s book, Lace of Country Streets:

The suburb is an obsolete and contradictory form of human settlement.


In the zone where city and country meet, place country roads at least a mile apart, so that they enclose squares of countryside and farmland at least one square mile in area. Build homesteads along these roads, one lot deep, on lots of at least half an acre, with the square mile of open countryside or farmland behind the houses.

Alexander doesn’t specify how wide this “zone where city and country meet” is, and if we’re got small cities every eight miles across an entire region, it would almost follow that these zones fill in the rest of the space between towns. If we take a square mile, and line it on all four sides with lots that are just over a half acre, we come up with 116 lots per square mile. If we multiply that by the average household size in the US of 2.58 persons per household, we get about 300 people per square mile in the countryside. If you multiply that by the 24,945 square miles covered by our region, you get 7,483,500 people. If you remove some to consider that a considerable portion of our region is the Chesapeake Bay and that some of those 24,945 square miles are already taken up by towns and, therefore, the Lace of Country Streets wouldn’t apply, it basically adds up to the rest of the people we were looking for.

So what we end up with is a pretty even population distribution across the entire region with a bit more concentrated in the many small towns and a lot more concentrated in the few big cities. but is this even distribution good for people or for the environment? I take issue with part of Alexander’s rationale for this pattern:

Two different necessities govern the distribution of population in a region. On the one hand, people are drawn to cities: they are drawn by the growth of civilization, jobs, education, economic growth, information. On the other hand, the region as a social and ecological whole will not be properly maintained unless the people of the region are fairly well spread out across it, living in many different kinds of settlements – farms, villages, towns, and cities – with each settlement taking care of the land around it. Industrial society has so far been following only the first of these necessities. People leave the farms and towns and villages and pack into the cities, leaving vast parts of the region depopulated and undermaintained.

But what does it mean to “take care of” and “maintain” the countryside? It seems to me that the countryside does pretty well without us up in its business. Alexander mentions the ecology of the city and how large cities are bad ecologically, but (a) some of Alexander’s patterns that I will discuss later address that and (b) by pulling people away from the countryside and concentrating them in cities, it allows for the countryside to function as what we need it most for (a carbon sink), and allows people to take advantage of shared walls and transit systems which greatly reduce our per-capita carbon footprint. If it were me, I’d distribute the population more like this:

Click to enlarge.

Click to enlarge.

Making all the big cities even bigger and, most importantly, denser, and leaving only small villages sprinkled throughout the countryside. As long as enough people live out there to grow the food and operate the mines for everyone else, there’s no reason to have everyone flung out across the landscape. The best thing we can do for the countryside really is to leave it alone. As far as getting people access to natural environments, we’ll talk about that soon, when I take a look at Alexander’s 3rd pattern, City Country Fingers.

Where I Should Live, According to Math

I don’t live in Washington, DC. I live near Washington, DC. I would like to live in it, but it’s an expensive city, and my income, while above the national average, is well below the regional average, and finding a two bedroom in our price range is difficult.

This got me thinking about affordable housing more broadly. For instance, where could I find a good, walkable neighborhood, anywhere in the country, that is within my price range? That got me started on my current project.

Using census data, I decided to map the variables of affordability and walkability. Affordability wasn’t hard; I mapped all the census tracts in the country that had a median income within $10,000 of mine, both above and below.Affordability

This shows me where I can afford to live, but a lot of the areas are rural places that I would never want to live in. My next task was to map walkability.

Walkability was harder to map. Even though Walkscore covers everywhere in America, it only offers it’s data in downloadable form for Washington, DC. So I downloaded the data, calculated the average Walkscore for census tracts in DC, downloaded virtually the entire American Community Survey, and compared the data therein to the average Walkscore to look for correlation. I found nineteen variables that had some significant correlation with Walkscore.VariablesI took each of these variables and gave them a score of one or zero, one if Walkscore would be above 70 at the value, or a zero if it would be below. Then I multiplied that score by each variables’ R-Square value, and added all the variables together to get a weighted Walkability score. I eliminated the bottom 50% of these values, and added the remainder to the map.Walkability

I was pretty happy with the result. With the exception of a few large tracts in western states, walkable places are where you would expect them to be; densely concentrated around major metropolitan areas

I intersected the two layers to get tracts that were both affordable and walkable.Intersected

This led to an interesting pattern: a few small, walkable town centers on the edge of metropolitan areas, but mostly urban neighborhoods outside of the downtown or in inner-ring suburbs.

However, it was still too many places to look at as a group, so I assigned a score to each tract based on how walkable and how affordable they are. I added these two together to get a combined score for what neighborhood would be best for us, based on these two criteria. In case you wanted the full equation for this score, it is

Combined score = (a – |a – b|) / a + ((if(c ≥ 373.6958, 1, 0) * 0.3153) + (if(d ≥ 21.2983, 1, 0) * 0.2725) + (if(e ≤ 38.8903, 1, 0) * 0.2803) + (if(f ≥ 68.0899, 1, 0) * 0.2971) + (if(g ≥ 67.4557, 1, 0) * 0.3350) + (if(h ≥ 59.9592, 1, 0) * 0.4048) + (if(i ≤31.4668, 1, 0) * 0.2529) + (if(j ≥ 65.5846, 1, 0) * 0.2734) + (if(k ≥ 65.3918, 1, 0) * 0.2839) + (if(l ≥ 58.6467, 1, 0) * 0.3533) + (if(m ≤35.7247, 1, 0) * 0.2576) + (if(n ≥226.8280, 1, 0) * 0.2763) + (if(o ≥78.1848,1, 0) * 0.2779) + (if(p ≥3.8273, 1, 0) * 0.2943) + (if(q ≥ 602.4307, 1, 0) * 0.2795) + (if(r ≤ 4.1293, 1, 0) * 0.2698) + (if(s ≥ 732.9079, 1, 0) * 0.2573) + (if(t ≥ 21.1155, 1, 0) *0.3974) + (if(u ≥82.4877, 1, 0) * 0.2810)) / 5.6596


a = Your Personal Income

Data for Each Tract from the American Community Survey:

b = Median Income

c = Nonrelatives in Household

d = % with at Least a Bachelor’s Degree

e = % Born in State of Residence

f = % 16 and Older in Labor Force

g = % 16 and Older in Civilian Labor Force

h = % 16 and Older Employed in Civilian Labor Force

i = % 16 and Older Not in Labor Force

j = % Females 16 and Older in Labor Force

k = % Females 16 and Older in Civilian Labor Force

l = % Females 16 and Older Employed in Civilian Labor Force

m = % 16 and Older Driving to Work Alone

n = Workers 16 and Older Walking to Work

o = Workers 16 and Older Commuting to Work by Other Means

p = % 16 and Older Commuting to Work by Other Means

q = Houses Built 1939 or Earlier

r = % 10-14 Years Old

s = Population 25-34 Years Old

t = % 25-34 Years Old

u = % 18 Years and Older

So, what got the highest score?

Capital Hill-01Capitol Hill, Seattle led the pack. To be honest, I was expecting something like a smaller, affordable Midwest town or something, but it the highest scoring areas were usually just outside of major downtowns. Other top areas included Cambridge and Somerville outside of Boston, and the South End in Boston; Columbia Heights, Washington, DC; The Mission District, Lower Haight, and Russian Hill, San Francisco; Midtown, Atlanta; Greenwood, Dyker Heights, Kensington, and Sheepshead Bay, Brooklyn; Graduate Hospital in Philadelphia, where we used to live; Lake View, Chicago; and Five Points, Denver.

Holly and I won’t be moving out of the region any time soon, but it’s good to have some idea of where to look if we decide to. And good to know that Columbia Heights is probably the neighborhood in DC for us, when the time comes. The formula isn’t perfect; it’s hard to control for things like how much of people’s income goes toward housing, and there is still a lot of wiggle room in these walkability measures. But it is a reasonable guideline that has provided interesting results.

UPDATE: I’ve gotten a few special requests for specific data on various areas, so I decided to make a little gallery of them below.

Density Without Mixed-use

P Street NW. From

Washington, DC is a world-class city. Beyond the monumental core, there are walkable, mixed-use neighborhoods of brightly colored rowhouses and tree-lined streets. Transit is extensive and generally reliable, and, barring further interference from the city council, is expanding in service. Although there are some things, such as the largely blanket height limit, that can get some planner’s goats, it is mostly an urbanist’s dream.

And because it’s so nice (and also because the height limit effectively limits housing supply), even those making above average incomes have trouble finding affordable housing here. With the average rent for a one-bedroom apartment downtown at over $2,000, many people are forced out onto the urban fringe. And that’s why I don’t live in Washington DC.

RoadI live here.

Arlington, Virginia, to be specific. And while it has taken some adjusting after living in Center City, Philadelphia, there has been one major difference that I’ve noticed between here and anywhere else I’ve lived:

Density CompTraditional cities are great places to walk. You have a lot of services, and a lot of residences close by to be served by them. It’s usually a bit frustrating driving, but you have so many other transportation options that it’s not really a loss.

The types of suburbs that I’ve grown up in have either been around slow-growth cities, such as Pittsburgh, or cities that never really had a tradition of density or regionalism anyway, like Provo, Utah. These suburbs have low housing densities, consisting almost entirely of single-family homes. Work is found in industrial or office parks, and shopping happens at strip malls. With all the uses separated, driving between them is pretty much the only reasonable way to get around. But since everything is at a much lower density, the traffic is only particularly bad on the main arterials.

What’s new to me about Washington suburbs (and particularly the inner ring) is that the demand for housing is high enough to necessitate high-density housing, but it was built in the era of single-use zoning, so the work and recreation are all far away. Like in the low-density suburbs, driving is usually the only option for getting around, but because of the higher density and the greater number of people, a huge amount of land becomes devoted to vehicle infrastructure. Even where it is possible to walk, the huge parking lots and wide roads make it undesirable.

King St-01

Seminary Rd-01Although I personally consider these environments largely unappealing, I think the fact that they already have the density to support mixed uses does make many of them decent candidates for suburban retrofitting, something I hope to examine more in later posts.

And it’s not like all of the DC region’s modern developments are devoid of urbanism. I’ll refer you to my friend Dan Reed, Silver Spring super booster, to learn about the ongoing urbanism there. Although Vishaan Chakrabarti calls it out for its traffic congestion in his book A Country of Cities (which, as John Norquist has argued, isn’t necessarily bad; places with a lot of traffic have traffic because people want to be there), Bethesda has a decent walkable core and strong mass transit connections to the rest of the region. And although the transition from single-family homes to high density urbanism is stark, and it has been described by some as “city-lite” (or worse, DC without all the poor minorities), the Rosslyn-Ballston corridor in Arlington is dense, mixed-use, and transit accessible.

Aerial view over Ballston, Arlington. From

And further afield, there are some areas that had the right idea but are a little lighter on execution. Reston, although suffering from a similar zoning-induced stark transition to that of Arlington, could be thought of as a “transit-ready” community with the upcoming opening of Metro’s Silver Line (although the station is a bit of a hike from Reston Town Center). And the New Urbanist darling of Kentlands, out on the edge of the region in Gaithersburg, is a pleasant, walkable community, even if transit options are limited and all of the commercial activity is just on one side of it.

The Washington, DC region, as evidenced by its high housing prices, is under-developed and, even where it is already dense, it is under-urbanized. But there are opportunities and, in some very small and limited ways, even the political will to fix things, hopefully for the better. I look forward to investigating urbanism in my new home and sharing it here, with you.

How Our Cities Keep Us Single (And Why That Has to Change) | ArchDaily

BIG’s Valentine’s Day installation in Times Square. From

This article from Vanessa Quirk is a little bit old, but I’m really glad I came across it, because it really gave me something to think about. In it, she brings up Desmond Morris’ comparison of the city, not to a concrete jungle, but a human zoo, where people are crammed together in small cages and where animals are less likely to breed.

Quirk discusses a number of issues that relate to this topic. Large cities provide an anonymity that makes it easy to form fleeting relationships and to break up. As humans, we have trouble relating to people outside of a small group–what some call the monkeysphere–and so the people we see in the city who are not part of our inner circle fade into the background.

Morris says that we prefer small, contained spaces where we can connect to people. Quirk cites the High Line in New York and the compact green spaces of Washington, DC as urban places that are more compatible to relationships. The point that she comes to is that “the description of a city designed for love – compact, walkable, with green, open spaces, and distinct neighborhoods (where people of a feather can flock, according to their tastes), is exactly the definition of a “healthy” modern city, where communities can thrive.”

It is a little hard for me to relate to some people, even my friends, as they look for love in the city. I got married when I was 22. The main reason is that I was lucky enough to find the right person at a young age, but it didn’t hurt that I come from a religion and a culture that emphasizes marriage and family, and that at the time I lived in a place where finding a spouse is strongly emphasized. But I know that the kinds of places Quirk describes are certainly places where I feel comfortable, and where I want to hang out with my friends, and especially my wife, and I can see how other people might use these same places as a space for relationships to flower.

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