{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T12:09:47Z","timestamp":1774181387762,"version":"3.50.1"},"reference-count":93,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>From physics to the social sciences, information is now seen as a fundamental component of reality. However, a form of information seems still underestimated, perhaps precisely because it is so pervasive that we take it for granted: the information encoded in the very environment we live in. We still do not fully understand how information takes the form of cities, and how our minds deal with it in order to learn about the world, make daily decisions, and take part in the complex system of interactions we create as we live together. This paper addresses three related problems that need to be solved if we are to understand the role of environmental information: (1) the physical problem: how can we preserve information in the built environment? (2) The semantic problem: how do we make environmental information meaningful? and (3) the pragmatic problem: how do we use environmental information in our daily lives? Attempting to devise a solution to these problems, we introduce a three-layered model of information in cities, namely environmental information in physical space, environmental information in semantic space, and the information enacted by interacting agents. We propose forms of estimating entropy in these different layers, and apply these measures to emblematic urban cases and simulated scenarios. Our results suggest that ordered spatial structures and diverse land use patterns encode information, and that aspects of physical and semantic information affect coordination in interaction systems.<\/jats:p>","DOI":"10.3390\/e20110834","type":"journal-article","created":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T11:55:41Z","timestamp":1540986941000},"page":"834","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Cities, from Information to Interaction"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4175-5701","authenticated-orcid":false,"given":"Vinicius M.","family":"Netto","sequence":"first","affiliation":[{"name":"Department of Urbanism, Universidade Federal Fluminense, Rua Passo da Patria 156, Niteroi, Rio de Janeiro 24210-240, Brazil"}]},{"given":"Edgardo","family":"Brigatti","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidade Federal do Rio de Janeiro (UFRJ), Av. Athos da Silveira Ramos 149, Rio de Janeiro 21941-972, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5951-1284","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Meirelles","sequence":"additional","affiliation":[{"name":"Laboratory on Human-Environment Relations in Urban Systems, Ecole Polytechnique Federale de Lausanne HERUS, EPFL, CH-1015 Lausanne, Switzerland"}]},{"given":"Fabiano L.","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Deparment of Physics (DFI), Universidade Federal de Lavras (UFLA), Caixa postal 3037, Lavras, Brazil"}]},{"given":"Bruno","family":"Pace","sequence":"additional","affiliation":[{"name":"Adalbertstra\u00dfe 66, PLZ 10179 Berlin, Germany"}]},{"given":"Caio","family":"Cacholas","sequence":"additional","affiliation":[{"name":"Programme of Graduate Studies, Universidade Federal Fluminense, Rua Passo da Patria 156, Niteroi, Rio de Janeiro 24210-240, Brazil"}]},{"given":"Patricia","family":"Sanches","sequence":"additional","affiliation":[{"name":"Department of Forest Science, Universidade de S\u00e3o Paulo, Avenida P\u00e1dua Dias 11, Piracicaba, S\u00e3o Paulo 13418-900, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Varela, F., Thompson, E., and Rosch, E. (1991). The Embodied Mind: Cognitive Science and Human Experience, The MIT Press.","DOI":"10.7551\/mitpress\/6730.001.0001"},{"key":"ref_2","unstructured":"Lakoff, G., and Johnson, M. (1999). Philosophy in the Flesh, Basic Books."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"625","DOI":"10.3758\/BF03196322","article-title":"Six views of embodied cognition","volume":"9","author":"Wilson","year":"2002","journal-title":"Psychon. Bull. Rev."},{"key":"ref_4","unstructured":"Robbins, P.E., and Aydede, M.E. (2009). The Cambridge Handbook of Situated Cognition, Cambridge University Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1093\/analys\/58.1.7","article-title":"The extended mind","volume":"58","author":"Clark","year":"1998","journal-title":"Analysis"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Portugali, J. (2011). Complexity, Cognition and the City, Springer Science & Business Media.","DOI":"10.1007\/978-3-642-19451-1"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/S0272-4944(03)00003-3","article-title":"The face of the city is its information","volume":"23","author":"Haken","year":"2003","journal-title":"J. Environ. Psychol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Haken, H., and Portugali, J. (2014). Information Adaptation: The Interplay Between Shannon Information and Semantic Information in Cognition, Springer.","DOI":"10.1007\/978-3-319-11170-4"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy systems","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_10","unstructured":"Shannon, C.E., and Weaver, W. (1949). Recent contributions to the mathematical theory of communication. The Mathematical Theory of Communication, The Illinois University Press."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kuppers, B.O. (2013). Elements of a Semantic Code. Evolution of Semantic Systems, Springer.","DOI":"10.1007\/978-3-642-34997-3_4"},{"key":"ref_12","unstructured":"Hinton, A. (2015). Understanding Context: Environment, Language, and Information Architecture, O\u2019Reilly Media, Inc."},{"key":"ref_13","unstructured":"Lynch, K. (1960). The Image of the City, The MIT Press."},{"key":"ref_14","unstructured":"Hillier, B. (1996). Space is the Machine, Cambridge University Press."},{"key":"ref_15","unstructured":"Brand, S. (1995). How Buildings Learn: What Happens After They\u2019re Built, Penguin Books."},{"key":"ref_16","unstructured":"Habermas, J. (1984). The Theory of Communicative Action, Polity Press."},{"key":"ref_17","unstructured":"Luhmann, N. (1995). Social Systems, Stanford University Press."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Hutchins, E. (1995). Cognition in the Wild, The MIT Press.","DOI":"10.7551\/mitpress\/1881.001.0001"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Stewart, J., Gapenne, O., and Paolo, E.D. (2010). Horizons for the enactive mind: Values, social interaction, and play. Enaction: Toward A New Paradigm for Cognitive Science, The MIT Press.","DOI":"10.7551\/mitpress\/9780262014601.001.0001"},{"key":"ref_20","unstructured":"Shannon, C.E., and Weaver, W. (1949). The Mathematical Theory of Communication, The Illinois University Press."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wiener, N. (1961). Cybernetics or Control and Communication in the Animal and the Machine, The MIT Press.","DOI":"10.1037\/13140-000"},{"key":"ref_22","unstructured":"Gleick, J. (2011). The Information: A History, A Theory, A Flood, Vintage."},{"key":"ref_23","first-page":"1971","article-title":"On the relationship between the second fundamental theorem of the mechanical theory of heat and probability calculations regarding the conditions for thermal equilibrium","volume":"17","author":"Boltzmann","year":"2015","journal-title":"Entropy"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"493","DOI":"10.3390\/e10040493","article-title":"Entropy and uncertainty","volume":"10","author":"Robinson","year":"2008","journal-title":"Entropy"},{"key":"ref_25","unstructured":"Prigogine, I., and Stengers, I. (1984). Order out of Chaos: Man\u2019s New Dialogue with Nature, Bantam Books."},{"key":"ref_26","unstructured":"Hidalgo, C. (2015). Why Information Grows: The Evolution of Order, from Atoms to Economies, Basic Books."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1002\/asi.20369","article-title":"Fundamental forms of information","volume":"57","author":"Bates","year":"2006","journal-title":"J. Am. Soc. Inf. Sci. Technol."},{"key":"ref_28","unstructured":"Cuadra, C., and Bates, M. (1974). Information and society. Library and Information Service Needs of the Nation: Proceedings of a Conference on the Needs of Occupational, Ethnic, and other Groups in the United States, ERIC."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Haken, H. (1988). Information and Self-Organization: A Macroscopic Approach to Complex Systems, Springer.","DOI":"10.1007\/978-3-662-07893-8"},{"key":"ref_30","unstructured":"Rapoport, A. (1982). The Meaning of the Built Environment, Sage."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hillier, B., and Hanson, J. (1984). The Social Logic of Space, Cambridge University Press.","DOI":"10.1017\/CBO9780511597237"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1037\/h0058700","article-title":"A decision-making theory of visual detection","volume":"61","author":"Tanner","year":"1954","journal-title":"Psychol. Rev."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/978-3-642-03832-7_12","article-title":"Evaluating the effectiveness and efficiency of visual variables for geographic information visualization","volume":"Volume 5756","author":"Garlandini","year":"2009","journal-title":"International Conference on Spatial Information Theory"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0006-8993(71)90358-1","article-title":"The hippocampus as a spatial map: Preliminary evidence from unit activity in the freely-moving rat","volume":"34","author":"Dostrovsky","year":"1971","journal-title":"Brain Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1038\/nature03721","article-title":"Microstructure of a spatial map in the entorhinal cortex","volume":"436","author":"Hafting","year":"2005","journal-title":"Nature"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1038\/s41586-018-0102-6","article-title":"Vector-based navigation using grid-like representations in artificial agents","volume":"557","author":"Banino","year":"2018","journal-title":"Nature"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s10339-007-0199-2","article-title":"On the assessment of landmark salience for human navigation","volume":"9","author":"Caduff","year":"2008","journal-title":"Cogn. Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/0010-0285(73)90004-2","article-title":"Perception in chess","volume":"4","author":"Chase","year":"1973","journal-title":"Cogn. Psychol."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Woodruff, A., Landay, J., and Stonebraker, M. (1998, January 24\u201327). Constant information density in zoomable interfaces. Proceedings of the working conference on Advanced Visual Interfaces, L\u2019Aquila, Italy.","DOI":"10.1145\/948496.948505"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1167\/7.2.17","article-title":"Measuring visual clutter","volume":"7","author":"Rosenholtz","year":"2007","journal-title":"J. Vis."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Portugali, J., Meyer, H., Stolk, E., and Tan, E. (2012). The genetic code for cities: Is it simpler than we think?. Complexity Theories of Cities Have Come of Age, Springer.","DOI":"10.1007\/978-3-642-24544-2"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Boeing, G. (2018). Urban Spatial Order: Street Network Orientation, Configuration, and Entropy. Phys. Soc.","DOI":"10.31235\/osf.io\/qj3p5"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1063\/1.166191","article-title":"Entropy estimation of symbol sequences","volume":"6","author":"Grassberger","year":"1996","journal-title":"Chaos An Interdiscip. J. Nonlinear Sci."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"046208","DOI":"10.1103\/PhysRevE.79.046208","article-title":"Entropy estimation of very short symbolic sequences","volume":"79","author":"Lesne","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"051104","DOI":"10.1103\/PhysRevE.67.051104","article-title":"Structural information in two-dimensional patterns: Entropy convergence and excess entropy","volume":"67","author":"Feldman","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Chen, Y., Wang, J., and Feng, J. (2017). Understanding the fractal dimensions of urban forms through spatial entropy. Entropy, 19.","DOI":"10.3390\/e19110600"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1126\/science.279.5347.39","article-title":"Is the geometry of nature fractal?","volume":"279","author":"Avnir","year":"1998","journal-title":"Science"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1038\/srep00812","article-title":"There is more than a power law in Zipf","volume":"2","author":"Cristelli","year":"2012","journal-title":"Sci. Rep."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"30011","DOI":"10.1209\/0295-5075\/90\/30011","article-title":"On the equivalence between stochastic baker\u2019s maps and two-dimensional spin systems","volume":"90","author":"Lindgren","year":"2010","journal-title":"EPL (Europhys. Lett.)"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1068\/a211447","article-title":"Urban Growth and Form: Scaling, Fractal Geometry, and Diffusion-limited Aggregation","volume":"21","author":"Batty","year":"1989","journal-title":"Environ. Plan. A"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Batty, M. (2013). The New Science of Cities, The MIT Press.","DOI":"10.7551\/mitpress\/9399.001.0001"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0272-4944(87)80020-8","article-title":"Exploring the anchorpoint hypothesis of spatial cognition","volume":"7","author":"Couclelis","year":"1987","journal-title":"J. Environ. Psychol."},{"key":"ref_53","unstructured":"Stern, E., and Portugali, J. (1999). Wayfinding Behavior: Cognitive Mapping and Other Spatial Processes, Johns Hopkins University Press."},{"key":"ref_54","unstructured":"Sommaruga, G. (2009). Philosophical Conceptions of Information. Formal Theories of Information: From Shannon to Semantic Information Theory and General Concepts of Information, Springer-Verlag."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1093\/bjps\/IV.14.147","article-title":"Semantic information","volume":"4","author":"Carnap","year":"1953","journal-title":"Br. J. Philos. Sci."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"MacKay, D.M. (1969). Information, Mechanism and Meaning, The MIT Press.","DOI":"10.7551\/mitpress\/3769.001.0001"},{"key":"ref_57","unstructured":"Barwise, J., and Perry, J. (1980). The Situation Underground, Stanford University Press."},{"key":"ref_58","unstructured":"Barwise, J., and Perry, J. (1983). Situations and Attitudes. Cambridge, The MIT Press."},{"key":"ref_59","unstructured":"Dretske, F.I. (1981). Knowledge and the Flow of Information, The MIT Press."},{"key":"ref_60","unstructured":"Devlin, K. (1991). Logic and Information, Cambridge University Press."},{"key":"ref_61","unstructured":"Gadamer, H.G. (1977). Philosophical Hermeneutics, University of California Press."},{"key":"ref_62","unstructured":"Garfinkel, H. (1984). Studies in Ethnomethodology, Polity Press."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/0010-0285(78)90006-3","article-title":"Distortions in judged spatial relations","volume":"10","author":"Stevens","year":"1978","journal-title":"Cogn. Psychol."},{"key":"ref_64","unstructured":"Passini, R. (1992). Wayfinding in Architecture, Van Nostrand Reinhold, Wiley."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Egenhofer, M., Giudice, N., Moratz, R., and Worboys, M. (2011). The social connection in mental representations of space: explicit and implicit evidence. International Conference on Spatial Information Theory, Springer.","DOI":"10.1007\/978-3-642-23196-4"},{"key":"ref_66","unstructured":"Roach, E., and Lloyd, B.B. (1978). Principles of categorization. Cognition and Categorization, Lawrence Erbaum Associates."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"519","DOI":"10.3758\/BF03199584","article-title":"The representation and integration in memory of spatial and nonspatial information","volume":"20","author":"McNamara","year":"1992","journal-title":"Mem. Cogn."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1037\/0278-7393.15.2.211","article-title":"Subjective hierarchies in spatial memory","volume":"15","author":"McNamara","year":"1989","journal-title":"J. Exp. Psychol. Learn. Mem. Cogn."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1037\/0033-295X.98.3.352","article-title":"Categories and particulars: Prototype effects in estimating spatial location","volume":"98","author":"Huttenlocher","year":"1991","journal-title":"Psychol. Rev."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1037\/0278-7393.32.3.333","article-title":"Global-scale location and distance estimates: Common representations and strategies in absolute and relative judgments","volume":"32","author":"Friedman","year":"2006","journal-title":"J. Exp. Psychol. Learn. Mem. Cogn."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1037\/0278-7393.12.2.182","article-title":"Effect of semantic clustering on the memory of spatial locations","volume":"12","author":"Hirtle","year":"1986","journal-title":"J. Exp. Psychol. Learn. Mem. Cogn"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0016-7185(92)90017-X","article-title":"Place recognition and wayfinding: Making sense of space","volume":"23","author":"Golledge","year":"1992","journal-title":"Geoforum"},{"key":"ref_73","unstructured":"de Faria, A.P.N., and Krafta, R. (2003, January 17\u201319). Representing urban cognitive structure through spatial differentiation. Proceedings of the 4th International Space Syntax Symposium, London, UK."},{"key":"ref_74","unstructured":"Popper, K.R. (1972). Objective knowledge: An Evolutionary Approach, Oxford University Press."},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Maraschin, C., and Krafta, R. (2013). Growth dynamic of retail locations: A methodological approach using a logistic model. Cybergeo: Eur. J. Geogr.","DOI":"10.4000\/cybergeo.26002"},{"key":"ref_76","first-page":"209","article-title":"The spatial dimensions of trade: From the geography of uses to the architecture of local economies","volume":"11","author":"Narvaez","year":"2014","journal-title":"ITU J. Fac. Archit."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"2119","DOI":"10.1016\/S1574-0080(04)80006-3","article-title":"Evidence on the nature and sources of agglomeration economies","volume":"Volume 4","author":"Rosenthal","year":"2004","journal-title":"Handbook of Regional and Urban Economics"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1111\/j.1468-0297.2005.00997.x","article-title":"Cities and specialisation: Evidence from South Asia","volume":"115","author":"Fafchamps","year":"2005","journal-title":"Econ. J."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.regsciurbeco.2008.08.005","article-title":"Using entropy measures to disentangle regional from national localization patterns","volume":"39","author":"Cutrini","year":"2009","journal-title":"Reg. Sci. Urban Econ."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/01638539909545067","article-title":"Indexical understanding of instructions","volume":"28","author":"Glenberg","year":"1999","journal-title":"Discourse Process."},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Egenhofer, M.J., Giudice, N., Moratz, R., and Worboys, M. (2011). Analyzing the spatial-semantic interaction of points of interest in volunteered geographic information. International Conference on Spatial Information Theory, Springer.","DOI":"10.1007\/978-3-642-23196-4"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/978-3-540-76876-0_9","article-title":"Algorithm, implementation and application of the SIM-DL similarity server","volume":"Volume 4853","author":"Fonseca","year":"2007","journal-title":"International Conference on GeoSpatial Sematics"},{"key":"ref_83","unstructured":"Campari, I., and Frank, A. (1993). Cognitive maps, cognitive collages, and spatial mental models. European Conference on Spatial Information Theory, Springer."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/S0004-3702(97)00083-0","article-title":"Pragmatic navigation: Reactivity, heuristics, and search","volume":"100","author":"Epstein","year":"1998","journal-title":"Artif. Intell."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Egenhofer, M.J., Giudice, N., Moratz, R., and Worboys, M. (2011). Spatial Information Theory: 10th International Conference, COSIT 2011, Belfast, ME, USA, Springer Science & Business Media.","DOI":"10.1007\/978-3-642-23196-4"},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Stewart, J., Gapenne, O., and Di Paolo, E. (2010). Foundational issues in enaction as a paradigm for cognitive science. Enaction: Toward A New Paradigm for Cognitive Science, The MIT Press.","DOI":"10.7551\/mitpress\/9780262014601.001.0001"},{"key":"ref_87","doi-asserted-by":"crossref","unstructured":"Stewart, J., Stewart, J.R., Gapenne, O., and Paolo, E.A.D. (2010). Enaction: Toward a New Paradigm for Cognitive Science, The MIT Press.","DOI":"10.7551\/mitpress\/9780262014601.001.0001"},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Netto, V.M., Meirelles, J., and Ribeiro, F.L. (2017). Social interaction and the city: The effect of space on the reduction of entropy. Complexity, 2017.","DOI":"10.31235\/osf.io\/kdfkt"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.physa.2015.03.021","article-title":"A one dimensional model of population growth","volume":"434","author":"Ribeiro","year":"2015","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_90","unstructured":"Allen, T. (1977). Managing the Flow of Technology, The MIT Press."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"160926","DOI":"10.1098\/rsos.160926","article-title":"A model of urban scaling laws based on distance dependent interactions","volume":"4","author":"Ribeiro","year":"2017","journal-title":"R. Soc. Open Sci."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1126\/science.1235823","article-title":"The origins of scaling in cities","volume":"340","author":"Bettencourt","year":"2013","journal-title":"Science"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1080\/19475683.2015.1009489","article-title":"Slipstreaming human geosimulation in virtual geographic environments","volume":"21","author":"Torrens","year":"2015","journal-title":"Ann. GIS"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/834\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:27:07Z","timestamp":1760196427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/834"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,31]]},"references-count":93,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["e20110834"],"URL":"https:\/\/doi.org\/10.3390\/e20110834","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201808.0426.v1","asserted-by":"object"},{"id-type":"doi","id":"10.20944\/preprints201808.0426.v2","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,31]]}}}