Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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


  1. Kempermann, G., Kuhn, H. G. & Gage, F. H. More hippocampal neurons in adult mice living in an enriched environment. Nature 386, 493–495 (1997).

    CAS  PubMed  ADS  Google Scholar 

  2. Hackman, D. A., Farah, M. J. & Meaney, M. J. Socioeconomic status and the brain: mechanistic insights from human and animal research. Nat. Rev. Neurosci. 11, 651–659 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  3. May, A. Experience-dependent structural plasticity in the adult human brain. Trends Cogn. Sci. 15, 475–482 (2011).

    PubMed  Google Scholar 

  4. Van Praag, H., Kempermann, G. & Gage, F. H. Neural consequences of environmental enrichment. Nat. Rev. Neurosci. 1, 191–198 (2000).

    PubMed  Google Scholar 

  5. Freund, J. et al. Emergence of individuality in genetically identical mice. Science 340, 756–759 (2013).

    CAS  PubMed  ADS  Google Scholar 

  6. Clemenson, G. D., Deng, W. & Gage, F. H. Environmental enrichment and neurogenesis: from mice to humans. Curr. Opin. Behav. Sci. 4, 56–62 (2015).

    Google Scholar 

  7. Kardan, O. et al. Neighborhood greenspace and health in a large urban center. Sci. Rep. 5, 11610 (2015).

    PubMed  PubMed Central  ADS  Google Scholar 

  8. Dadvand, P. et al. Green spaces and cognitive development in primary schoolchildren. Proc. Natl Acad. Sci. USA 112, 7937–7942 (2015).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  9. Engemann, K. et al. Residential green space in childhood is associated with lower risk of psychiatric disorders from adolescence into adulthood. Proc. Natl Acad. Sci. USA 116, 5188–5193 (2019).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  10. Berman, M. G., Stier, A. J. & Akcelik, G. N. Environmental neuroscience. Am. Psychol. 74, 1039–1052 (2019).

    PubMed  Google Scholar 

  11. Bratman, G. N. et al. Nature and mental health: an ecosystem service perspective. Sci. Adv. 5, eaax0903 (2019).

    PubMed  PubMed Central  ADS  Google Scholar 

  12. Lederbogen, F. et al. City living and urban upbringing affect neural social stress processing in humans. Nature 474, 498–501 (2011).

    CAS  PubMed  Google Scholar 

  13. Kühn, S. et al. In search of features that constitute an “enriched environment” in humans: Associations between geographical properties and brain structure. Sci. Rep. 7, 11920 (2017).

    PubMed  PubMed Central  ADS  Google Scholar 

  14. Carey, I. M. et al. Are noise and air pollution related to the incidence of dementia? A cohort study in London, England. BMJ Open 8, e022404 (2018).

    PubMed  PubMed Central  Google Scholar 

  15. Stier, A. et al. Rethinking depression in cities: evidence and theory for lower rates in larger urban areas. Preprint at (2020).

  16. Coutrot, A. et al. Global determinants of navigation ability. Curr. Biol. 28, 2861–2866 (2018).

    CAS  PubMed  Google Scholar 

  17. Malanchini, M. et al. Evidence for a unitary structure of spatial cognition beyond general intelligence. npj Sci. Learn. 5, 9 (2020).

    PubMed  PubMed Central  Google Scholar 

  18. Spiers, H. J. & Maguire, E. A. Thoughts, behaviour, and brain dynamics during navigation in the real world. Neuroimage 31, 1826–1840 (2006).

    PubMed  Google Scholar 

  19. Maguire, E. A., Woollett, K. & Spiers, H. J. London taxi drivers and bus drivers: a structural MRI and neuropsychological analysis. Hippocampus 16, 1091–1101 (2006).

    PubMed  Google Scholar 

  20. Xu, J. et al. Global urbanicity is associated with brain and behaviour in young people. Nat. Hum. Behav. (2021).

  21. Coutrot, A. et al. Virtual navigation tested on a mobile app is predictive of real-world wayfinding navigation performance. PLoS ONE 14, e0213272 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  22. Spiers, H. J., Coutrot, A. & Hornberger, M. Explaining world-wide variation in navigation ability from millions of people: citizen science project Sea Hero Quest. Top. Cogn. Sci. (2021).

  23. Sutherland, R. J. & Hamilton, D. A. Rodent spatial navigation: at the crossroads of cognition and movement. Neurosci. Biobehav. Rev. 28, 687–697 (2004).

    PubMed  Google Scholar 

  24. Epstein, R. A., Patai, E. Z., Julian, J. B. & Spiers, H. J. The cognitive map in humans: spatial navigation and beyond. Nat. Neurosci. 20, 1504 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. Boeing, G. OSMnx: new methods for acquiring, constructing, analyzing, and visualizing complex street networks. Comput. Environ. Urban Syst. 65, 126–139 (2017).

    Google Scholar 

  26. Coughlan, G. et al. Toward personalized cognitive diagnostics of at-genetic-risk Alzheimer’s disease. Proc. Natl Acad. Sci. USA 116, 9285–9292 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  27. Klencklen, G., Després, O. & Dufour, A. What do we know about aging and spatial cognition? Reviews and perspectives. Ageing Res. Rev. 11, 123–135 (2012).

    PubMed  Google Scholar 

  28. Lester, A. W., Moffat, S. D., Wiener, J. M., Barnes, C. A. & Wolbers, T. The aging navigational system. Neuron 95, 1019–1035 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  29. Nazareth, A., Huang, X., Voyer, D. & Newcombe, N. A meta-analysis of sex differences in human navigation skills. Psychon. Bull. Rev. 26, 1503–1528 (2019).

    PubMed  Google Scholar 

  30. Ritchie, S. J. & Tucker-Drob, E. M. How much does education improve intelligence? A meta-analysis. Psychol. Sci. 29, 1358–1369 (2018).

    PubMed  PubMed Central  Google Scholar 

  31. Ulrich, S., Grill, E. & Flanagin, V. L. Who gets lost and why: a representative cross-sectional survey on sociodemographic and vestibular determinants of wayfinding strategies. PLoS ONE 14, e0204781 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  32. Fuchs, F. et al. Exposure to an enriched environment up to middle age allows preservation of spatial memory capabilities in old age. Behav. Brain Res. 299, 1–5 (2016).

    PubMed  Google Scholar 

  33. Lynch, K. The Image of the City (The MIT Press, 1960).

  34. Marshall, S. Streets and Patterns (Spon Press, 2005).

  35. Watts, A., Ferdous, F., Diaz Moore, K. & Burns, J. M. Neighborhood integration and connectivity predict cognitive performance and decline. Gerontol. Geriatr. Med. (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  36. Koohsari, M. J. et al. Cognitive function of elderly persons in Japanese neighborhoods: the role of street layout. Am. J. Alzheimers Dis. Other Demen. 34, 381–389 (2019).

    PubMed  PubMed Central  Google Scholar 

  37. Bongiorno, C. et al. Vector-based pedestrian navigation in cities. Nat. Comput. Sci. 1, 678–685 (2021).

    Google Scholar 

  38. Boeing, G. A multi-scale analysis of 27,000 urban street networks: every US city, town, urbanized area, and Zillow neighborhood. Environ. Plann. B Urban Anal. City Sci. 47, 590–608 (2018).

    Google Scholar 

  39. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948).

    MathSciNet  MATH  Google Scholar 

  40. Barthélemy, M. Spatial networks. Phys. Rep. 499, 1–101 (2011).

    MathSciNet  ADS  Google Scholar 

  41. Gudmundsson, A. & Mohajeri, N. Entropy and order in urban street networks. Sci. Rep. 3, 3324 (2013).

    PubMed  PubMed Central  ADS  Google Scholar 

  42. Batty, M., Morphet, R., Masucci, P. & Stanilov, K. Entropy, complexity, and spatial information. J. Geogr. Syst. 16, 363–385 (2014).

    PubMed  PubMed Central  Google Scholar 

  43. Boeing, G. Urban spatial order: street network orientation, configuration, and entropy. Appl. Netw. Sci. 67, 1–20 (2019).

    Google Scholar 

  44. McNamee, D., Wolpert, D. & Lengyel, M. Efficient state-space modularization for planning: theory, behavioral and neural signatures. In Advances in Neural Information Processing Systems 29 (NIPS 2016) (eds Lee. D. et al.) 4511–4519 (Curran Associates, 2016).

  45. Wiener, J. M., Schnee, A. & Mallot, H. A. Use and interaction of navigation strategies in regionalized environments. J. Env. Psychol. 24, 475–493 (2004).

    Google Scholar 

  46. Brunyé, T. T. et al. Strategies for selecting routes through real-world environments: Relative topography, initial route straightness, and cardinal direction. PLoS ONE 10, e0124404 (2015).

    PubMed  PubMed Central  Google Scholar 

  47. Ekstrom, A. D., Spiers, H. J., Bohbot, V. D. & Rosenbaum, R. S. Human Spatial Navigation (Princeton University Press, 2018).

  48. Salon, D. Heterogeneity in the relationship between the built environment and driving: focus on neighborhood type and travel purpose. Res. Transp. Econ. 52, 34–45 (2015).

    Google Scholar 

  49. Lenormand, M., Bassolas, A. & Ramasco, J. J. Systematic comparison of trip distribution laws and models. J. Transp. Geogr. 51, 158–169 (2016).

    Google Scholar 

  50. Nazareth, A., Weisberg, S. M., Margulis, K. & Newcombe, N. S. Charting the development of cognitive mapping. J. Exp. Child Psychol. 170, 86–106 (2018).

    PubMed  Google Scholar 

  51. Montello, D. R. A conceptual model of the cognitive processing of environmental distance information. In Spatial Information Theory: 9th International Conference, COSIT 2009 (eds. Hornsby, K. S. et al.) 1–17 (Springer, 2009).

  52. Masucci, A. P., Arcaute, E., Hatna, E., Stanilov, K. & Batty, M. On the problem of boundaries and scaling for urban street networks. J. R. Soc. Interface 12, 20150763 (2015).

    PubMed  PubMed Central  Google Scholar 

  53. Giacomin, D. J. & Levinson, D. M. Road network circuity in metropolitan areas. Environ. Plann. B Plann. Des. 42, 1040–1053 (2015).

    Google Scholar 

  54. Jiang, B. & Claramunt, C. Topological analysis of urban street networks. Environ. Plann. B Plann. Des. 31, 151–162 (2004).

    Google Scholar 

  55. Porta, S. et al. Street centrality and densities of retail and services in Bologna, Italy. Environ. Plann. B Plann. Des. 36, 450–465 (2009).

    Google Scholar 

  56. Javadi, A.-H. et al. Hippocampal and prefrontal processing of network topology to simulate the future. Nat. Commun. 8, 14652 (2017).

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  57. Jiang, B. & Claramunt, C. A structural approach to the model generalization of an urban street network. GeoInformatica 8, 157–171 (2004).

    Google Scholar 

  58. Filomena, G., Verstegen, J. A. & Manley, E. A computational approach to ‘The Image of the City’. Cities 89, 14–25 (2019).

    Google Scholar 

  59. Mou, W., McNamara, T. P., Valiquette, C. M. & Rump, B. Allocentric and egocentric updating of spatial memories. J. Exp. Psychol. Learn. Mem. Cogn. 30, 142 (2004).

    PubMed  Google Scholar 

  60. Tversky, B. Distortions in memory for maps. Cogn. Psychol. 13, 407–433 (1981).

    Google Scholar 

  61. Sadalla, E. K. & Magel, S. G. The perception of traversed distance. Environ. Behav. 12, 65–79 (1980).

    Google Scholar 

  62. Spiers, H. J. & Maguire, E. A. A navigational guidance system in the human brain. Hippocampus 17, 618–626 (2007).

    PubMed  PubMed Central  Google Scholar 

  63. Howard, L. R. et al. The hippocampus and entorhinal cortex encode the path and Euclidean distances to goals during navigation. Curr. Biol. 24, 1331–1340 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  64. Spiers, H. J. & Barry, C. Neural systems supporting navigation. Curr. Opin. Behav. Sci. 1, 47–55 (2015).

    Google Scholar 

  65. Douglas, D. H. & Peucker, T. K. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica 10, 112–122 (1973).

    Google Scholar 

  66. Hentschke, H. & Stüttgen, M. C. Computation of measures of effect size for neuroscience data sets. Eur. J. Neurosci. 34, 1887–1894 (2011).

    PubMed  Google Scholar 

Download references


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.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

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.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing