Urban spatial order: street network orientation, configuration, and entropy

Abstract

Street networks may be planned according to clear organizing principles or they may evolve organically through accretion, but their configurations and orientations help define a city's spatial logic and order. Measures of entropy reveal a city's streets' order and disorder. Past studies have explored individual cases of orientation and entropy, but little is known about broader patterns and trends worldwide. This study examines street network orientation, configuration, and entropy in 100 cities around the world using OpenStreetMap data and OSMnx. It measures the entropy of street bearings in weighted and unweighted network models, 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. A cluster analysis is performed to explore similarities and differences among these study sites in multiple dimensions. Significant statistical relationships exist between city orientation-order and other indicators of spatial order, including street circuity and measures of connectedness. On average, US/Canadian study sites are far more grid-like than those elsewhere, exhibiting less entropy and circuity. These indicators, taken in concert, help reveal the extent and nuance of the grid. These methods demonstrate automatic, scalable, reproducible tools to empirically measure and visualize city spatial order, illustrating complex urban transportation system patterns and configurations around the world.

Street Network Models and Measures for Every U.S. City, County, Urbanized Area, Census Tract, and Zillow-Defined Neighborhood

“…These measures are described in Table 1 and extended technical definitions and mathematical derivations can be found in [3,16,32,45,48,51,73,[91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106]. Note that we distinguish between "edges" and physical "streets" in certain instances to not double-count bidirectional streets with reciprocal edges pointing in both directions.…”

Spatial Information and the Legibility of Urban Form: Big Data in Urban Morphology

“…Spatial information plays an important role in urban simulation for community visioning (Vanegas, Aliaga, Benes, & Waddell, 2009;Waddell et al, 2018), streetscape quality analysis (Shen et al, 2018), and predicting urban attributes from street imagery (Arietta, Efros, Ramamoorthi, & Agrawala, 2014). Another research stream examines the spatial ordering of cities' configuration and orientation through circulation network patterns (2014, Barthelemy, Bordin, Berestycki, & Gribaudi, 2013;Barthelemy, 2017;Boeing, 2019;Buhl et al, 2006;Chan, Donner, & Lämmer, 2011;Courtat, Gloaguen, & Douady, 2011;Louf & Barthelemy, 2014;Mohajeri & Gudmundsson, 2012;Mohajeri, French, & Batty, 2013). Various spatial logics and ordering principles exist in planned, unplanned, formal, informal, gridded, and organic urban patterns (Kostof, 1991;Rose-Redwood & Bigon, 2018;Smith, 2007) and a city without one single, formal, geometric ordering logic may have well-defined, high-functioning physical and social structure (Hanson, 1989).…”

“…The second method uses rose diagrams of street orientations to visualize the spatial ordering of urban circulation infrastructure , 2013bMohajeri & Gudmundsson, 2014;Mohajeri, French, & Gudmundsson, 2013). First we calculate the compass bearings of all the street segments in 25 world cities, then visualize them with a rose diagram in which the bars' directions represent 10°bins around the compass, and the bars' lengths represent the relative frequency of street segments that fall in each bin (Boeing, 2019). This produces a visual representation of the extent to which a street network follows the spatial ordering logic of a low entropy grid versus having streets oriented more evenly in all compass directions.…”

“…International Journal of Information Management xxx (xxxx) xxx-xxx theoretical development see Boeing, 2019). For example, in Manhattan's rose diagram we can see the spatial order produced by its dominant orthogonal grid (cf.…”

Classification of Urban Street Networks Based on Tree-Like Network Features

“…Marshall, Gil et al used a large amount of data and a variety of analysis methods to study the street network, proposed a network modeling method, and outlined the main street network model features and the complex relationship between different network models [18]. Boeing s research on the structure of street networks, which calculates the structural indicators of street networks around the world and classifies them into clusters, helped to reveal the scope and nuances of street networks [19]. Shi and Wang believed that the street network structure is not simply a hierarchical, connection, or layout structure, but an organic combination of the three [20].…”