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Entropy of city street networks linked to future spatial navigation ability


The cultural and geographical properties of the environment have been shown to deeply influence cognition and mental health1,2,3,4,5,6. Living near green spaces has been found to be strongly beneficial7,8,9,10,11, and urban residence has been associated with a higher risk of some psychiatric disorders12,13,14—although some studies suggest that dense socioeconomic networks found in larger cities provide a buffer against depression15. However, how the environment in which one grew up affects later cognitive abilities remains poorly understood. Here we used a cognitive task embedded in a video game16 to measure non-verbal spatial navigation ability in 397,162 people from 38 countries across the world. Overall, we found that people who grew up outside cities were better at navigation. More specifically, people were better at navigating in environments that were topologically similar to where they grew up. Growing up in cities with a low street network entropy (for example, Chicago) led to better results at video game levels with a regular layout, whereas growing up outside cities or in cities with a higher street network entropy (for example, Prague) led to better results at more entropic video game levels. This provides evidence of the effect of the environment on human cognition on a global scale, and highlights the importance of urban design in human cognition and brain function.

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Fig. 1: Wayfinding task.
Fig. 2: SNE and environment effect in 38 countries.
Fig. 3: Comparison of SNE with other measures of city complexity.
Fig. 4: Participants are accurate at navigating more entropic game levels when they grew up in more entropic environments.

Data availability

A dataset with the preprocessed trajectory lengths and demographic information is available at Owing to its considerable size (around 1 terabyte), the dataset with the full trajectories is available on a dedicated server: We also set up a portal where researchers can invite a targeted group of participants to play SHQ and generate data about their spatial navigation capabilities. Those invited to play the game will be sent a unique participant key, generated by the SHQ system according to the criteria and requirements of a specific project. Access to the portal will be granted for non-commercial purposes. Future publications based on this dataset should add ‘Sea Hero Quest Project’ as a co-author.

Code availability

The Python and MATLAB (R2018a) code that allows the presented analyses to be reproduced is available along the preprocessed trajectory lengths and demographic information at


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This research is part of the Sea Hero Quest initiative funded and supported by Deutsche Telekom. Alzheimer’s Research UK (ARUK-DT2016-1) funded the analysis; Glitchers designed and produced the game; and Saatchi and Saatchi London managed the creation of the game. The geographical information used in this study has been made available by OSM contributors under the Open Database License (

Author information

Authors and Affiliations



H.J.S., M.H. and A.C. supervised the project. H.J.S., M.H., A.C., S.G., C.G., R.C.D., J.M.W. and C.H. designed the research. A.C., E.M., G.F. and D.Y. analysed data. A.C., E.M. and H.J.S. wrote the paper.

Corresponding authors

Correspondence to A. Coutrot or H. J. Spiers.

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The authors declare no competing interests.

Peer review

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Nature thanks Marc Berman, Luis Bettencourt, Mary Hegarty, Nora Newcombe and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Colour-coded world maps.

a, Sample size. b, Proportion of city participants. c, Environment effect size computed from a LMM predicting wayfinding performance, with fixed effects for age, gender and education, and random environment slopes clustered by country. The environment effect sizes are the environment slopes clustered by country, identical to the values in Fig. 2a.

Extended Data Fig. 2 Association between age, home environment, country and path integration performance.

a, Path integration performance as a function of age for male and female participants who grew up in city and non-city environments. Path integration performance is averaged within 5-year windows, centre values correspond to the means. b, Difference of the effect of growing up outside cities on path integration performance across countries. We fit a logistic mixed model for path integration performance, with fixed effects for age, gender and education, and random environment slopes clustered by country, see Supplementary Methods. Positive values indicate an advantage for participants raised outside cities. c, SNE as a function of the environment effect size (random environment slope) in each country, as in Fig. 2b, see Supplementary Methods. All error bars correspond to standard errors, n = 182,122 participants.

Extended Data Fig. 3 Environment effect size across age, gender and level of education.

Effect size is quantified with Hedge’s g, within five-year windows. Positive values correspond to an advantage for participants who grew-up outside cities. Error bars correspond to 95% CI and the centre values correspond to the means.

Extended Data Fig. 4 Wayfinding performance in city and non-city environments across age, in each country.

Wayfinding performance is averaged within 10-year windows. Error bars correspond to standard errors and centre values correspond to the means. Note that these values correspond to raw wayfinding performance; that is, they have not been corrected for age, gender or education. Note: Vietnam and Albania y axis lower bound is 0 to allow display of data points, instead of 0.5 for the rest of the countries. Altogether, we included n = 397,162 participants.

Extended Data Fig. 5 Examples of city street networks.

a, The road networks of New York City (USA, right) and London (UK, left) have been partitioned using the Louvain community detection algorithm on the dual graph, setting edge cost as angular change. The road networks within a 3 × 3 km2 box around the city centres are represented. b, Street network of the 10 biggest cities in terms of population in Argentina and in Romania. We used OSMnx to gather the “drive” OSM network within 1,000 × 1,000-m2 boxes around each city centre. The reasons behind these differences are mostly historical. In South America, grid city design is characteristic of Hispanic American colonization, while disorganized street networks correspond to the typical organic street pattern of old European city cores.

Extended Data Fig. 6 Association between GDP per capita and SNE in City Hero Quest, a city-themed version of Sea Hero Quest.

a, GDP per capita as a function of SNE. b, Screenshot from SHQ (left) and CHQ (right). c, Subset of SHQ levels used in the second experiment run on Prolific. d, CHQ levels used in the second experiment.

Extended Data Fig. 7 Association between age, home environment, country and wayfinding performance.

a, Wayfinding performance as a function of age for participants who grew up in city, suburb, mixed and rural environments. Data points correspond to the wayfinding performance averaged within 5-year windows. b, Difference in the effect of growing up outside cities on wayfinding performance across countries. We fit a linear mixed model for wayfinding performance, with fixed effects for age, gender and education, and random environment slopes clustered by country, as in Fig. 2a. Suburbs, mixed and rural environment slopes are represented, with City environment as baseline. Positive values correspond to an advantage compared to growing up in cities. Countries are ranked according to their suburb slope. The slopes of the different non-city environments are highly correlated: Pearson’s r(suburb, mixed) = 0.97, p < 0.001, r(suburb, rural) = 0.72, p < 0.001, r(mixed, rural) = 0.53, p < 0.001. The country ranking is very similar to the one with only 2 classes (city / non-city): Spearman’s r(non-city, suburb) = 0.85, p < 0.001, r(non-city, mixed) = 0.73, p < 0.001, r(non-city, rural) = 0.94, p < 0.001. P values are from a t-test testing the hypothesis of no correlation against the alternative hypothesis of a nonzero correlation. c, Pairwise differences between random environment slopes shown in panel b, averaged over countries. We show that the average difference in effect size between the city environment and the other 3 environments (city-rural, city-mixed, city-suburb) are around 10 times larger than the difference between the ‘non-city’ environments (rural-mixed, mixed-suburb, rural-suburb). This supports the approach to cluster together rural, mixed and suburb environments. All error bars correspond to standard errors, n = 397,162 participants.

Extended Data Fig. 8 Environment effect size and city complexity measures in high-SNE and low-SNE countries.

In each of the 380 included cities we computed a range of metrics to quantify different aspects of its complexity. We then took an average of these metrics weighted by the city population to have one value per country. We normalized these values by dividing them by their maximum. Network-based metrics - On top of the SNE used in this study, we computed other graph-theoretic measures commonly considered for spatial analysis of cities: average street length, circuity, neighbourhood degree, clustering coefficient, closeness centrality, betweenness centrality, and degree centrality. Route-based metrics - we simulated 1,000 routes in each city, and quantified five key variables derived from each route: number of unique streets, number of transitions in the partitions in street network structure, deviation from regular 90° turns at each turn, overall deviation from the target and number of turns above 50°. Individual data points correspond to countries (n = 38). In the box plots, the horizontal bar represents the sample median, the hinges represent the first and third quartiles, and the whiskers extend from the hinges to the largest/lowest value no further than ±1.5 × IQR from the hinge (where IQR is the inter-quartile range).

Extended Data Fig. 9 SNE across reported home environments.

SNE computed at the home addresses of the 599 participants to the follow-up experiment CHQ as a function of the reported type of home environment. The size of the square boxes used to compute the SNE were adjusted for the average street density within each reported environment (see Supplementary Methods). Error bars correspond to standard errors and centre values correspond to the means.

Extended Data Fig. 10 Estimation of the robustness of the Pearson’s correlation between SNE and environment effect size.

Bootstrapped correlation coefficients computed from 1,000 resampling with replacement. a, Histogram of the computed correlation coefficients. We obtained r = −0.60, 95% CI = [−0.78 −0.30]. b, Regression lines for each sample. c, Pearson’s correlation between environment effect size and different SNE calculations. The SNE set in bold is the one used in this manuscript. OSM = OpenStreetMaps, GM = Google Maps. P values are from a t-test testing the hypothesis of no correlation against the alternative hypothesis of a nonzero correlation.

Supplementary information

Supplementary Information

This file contains Supplementary Discussion; Supplementary Notes; Supplementary Methods and Supplementary References

Reporting Summary

Supplementary Table 1

For each country, the number of participants included in the analysis (N), their mean age and standard deviation, the proportion of male versus female individuals, tertiary versus secondary education, city versus non-city home environment.

Supplementary Table 2

For each country, the 10 biggest cities in term of population with their route-based metrics (unique streets, crossed partitions, turns above 50°, snap deviation, target deviation) and their network-based metrics (SNE, street length, circuity, neighbourhood degree, clustering coefficient, closeness centrality, betweenness centrality, degree centrality).

Peer Review File

Supplementary Video 1

Examples of navigation in two Sea Hero Quest levels: level 27 (left) and level 58 (right).

Supplementary Video 2

Example of navigation in one City Hero Quest level.

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Coutrot, A., Manley, E., Goodroe, S. et al. Entropy of city street networks linked to future spatial navigation ability. Nature 604, 104–110 (2022).

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