My new article, Urban Spatial Order: Street Network Orientation, Configuration, and Entropy, has just been published in one of my favorite journals: Applied Network Science (download free PDF). This study explores the spatial signatures of urban evolution and central planning. It examines street network orientation, connectivity, granularity, and entropy in 100 cities around the world using OpenStreetMap data and OSMnx for modeling and visualization:

So, who’s got a grid and who doesn’t? Each of the cities above is represented by a polar histogram (aka rose diagram) depicting how its streets orient. Each bar’s direction represents the compass bearings of the streets (in that histogram bin) and its length represents the relative frequency of streets with those bearings. The cities above are in alphabetical order. Here they are again, re-sorted from most-ordered/gridded city (Chicago) to most-disordered (Charlotte):

Note that these are cities proper (municipalities), not wider metro areas or urban agglomerations. Some cities, like Seattle, Denver, and Minneapolis, have an offset downtown with a relatively small number of streets, but the rest of the city’s much larger volume of streets swamps the histogram’s relative frequencies. Above, we can see that Chicago is the most grid-like city here and Charlotte is the least. To illustrate this more clearly, in Manhattan for example, we can easily see the angled, primarily orthogonal street grid in its polar histogram:

Unlike most American cities that have one or two primary street grids organizing city circulation, Boston’s streets are more evenly distributed in every direction. Although it features a grid in some neighborhoods like the Back Bay and South Boston, these grids tend to not be aligned with one another, resulting in a mish-mash of competing orientations. If you’re going north and then take a right turn, you might know that you are immediately heading east, but it’s hard to know where you’re eventually really heading in the long run. What Boston lacks in legible circulation patterns, it makes up for in other Lynchian elements (paths, edges, districts, nodes, landmarks) that help make it an “imageable” city for locals and visitors.

This study measures the entropy (or disordered-ness) of street bearings in each street network, along with each city’s typical street segment length, average circuity, average node degree, and the network’s proportions of four-way intersections and dead-ends. It also develops a new indicator of orientation-order that quantifies how a city’s street network follows the geometric ordering logic of a single grid. These indicators, taken in concert, reveal the extent and nuance of the grid.

Across these study sites, US/Canadian cities have an average orientation-order nearly thirteen-times greater than that of European cities, alongside nearly double the average proportion of four-way intersections. Meanwhile, these European cities’ streets on average are 42% more circuitous than those of the US/Canadian cities. North American cities are far more grid-like than cities in the rest of the world and exhibit far less orientation entropy and street circuity. We can see this with a cluster analysis to explore similarities and differences among these study sites in multiple dimensions (full methodological details in paper):

The clustering dendrogram above shows how different cities’ street networks group together in similarity. We can also visualize this in two dimensions using t-SNE, a manifold learning approach for nonlinear dimensionality reduction. Here is a scatterplot of cities in two dimensions via t-SNE, with cluster colors corresponding to those above (triangles represent US/Canadian cities and circles represent other cities):

Most of the North American cities lie near each other in three adjacent clusters (red, orange, and blue), which contain grid-like—and almost exclusively North American—cities. The orange cluster represents relatively dense, gridded cities like Chicago, Portland, Vancouver, and Manhattan. The blue cluster contains less-perfectly gridded US cities, typified by San Francisco and Washington (plus, interestingly, Buenos Aires). The red cluster represents sprawling but relatively low-entropy cities like Los Angeles, Phoenix, and Las Vegas.

Sprawling, high-entropy Charlotte is in a separate cluster (alongside Honolulu) dominated by cities that developed at least in part under the auspices of 20th century communism, including Moscow, Kiev, Warsaw, Prague, Berlin, Kabul, Pyongyang, and Ulaanbaatar. Beijing and Shanghai are alone in their own cluster, more dissimilar from the other study sites. The dark gray cluster comprises the three cities with the most circuitous networks: Caracas, Hong Kong, and Sarajevo. While the US cities tend to group together in the red, orange, and blue clusters, the other world regions’ cities tend to distribute more evenly across the green, purple, and light gray clusters.

For more information on my methodology and findings, check out the open-access article, or check out OSMnx for the Python tool used for these analyses and visualizations. Some of my preliminary work on this (and links to source code) appears in two blog posts from last summer.