Skip to main content
SpringerLink
Log in

Cities as Complex Systems: Scaling, Interaction, Networks, Dynamics and Urban Morphologies

  • Reference work entry
Encyclopedia of Complexity and Systems Science

Definition of the Subject

Cities have been treated as systems for fifty years but only in the last two decades has the focus changed from aggregateequilibrium systems to more evolving systems whose structure emerges from the bottom up. We firstoutline the rudiments of the traditional approach focusing on equilibrium and then discuss how the paradigm has changed to one which treats cities asemergent phenomena generated through a combination of hierarchical levels of decision, driven in decentralized fashion. This is consistent with thecomplexity sciences which dominate the simulation of urban form and function. We begin however with a review of equilibrium models, particularlythose based on spatial interaction, and we then explore how simple dynamic frameworks can be fashioned to generate more realistic models. In exploringdynamics , nonlinear systems which admit chaos and bifurcation have relevance but recently more pragmaticschemes of structuring urban...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 3,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

Agent‐based models:

Systems composed of individuals who act purposely in making locational/spatial decisions.

Bifurcation:

A process whereby divergent paths are generated in a trajectory of change in an urban system.

City size distribution:

A set of cities ordered by size, usually population, often in rank order.

Emergent patterns:

Land uses or economic activities which follow some spatial order.

Entropy maximizing:

The process of generating a spatial model by maximizing a measure of system complexity subject to constraints.

Equilibrium:

A state of the urban system which is balanced and unchanging.

Exponential growth:

The process whereby an activity changes through positive feedback on itself.

Fast dynamics:

A process of frequent movement between locations, often daily.

Feedback:

The process whereby a system variable influences another variable, either positively or negatively.

Fractal structure:

A pattern or arrangement of system elements that are self‐similar at different spatial scales.

Land use transport model:

A model linking urban activities to transport interactions.

Life cycle effects:

Changes in spatial location which are motivated by aging of urban activities and populations.

Local neighborhood:

The space immediately around a zone or cell.

Logistic growth:

Exponential growth capacitated so that some density limit is not exceeded.

Lognormal distribution:

A distribution which has fat and long tails which is normal when examined on a logarithmic scale.

Microsimulation:

The process of generating synthetic populations from data which is collated from several sources.

Model validation:

The process of calibrating and testing a model against data so that its goodness of fit is optimized.

Multipliers:

Relationships which embody nth order effects of one variable on another.

Network scaling:

The in‐degrees and out‐degrees of a graph whose nodal link volumes follow a power law.

Population density profile:

A distribution of populations which typically follows an exponential profile when arrayed against distance from some nodal point.

Power laws:

Scaling laws that order a set of objects according to their size raised to some power.

Rank size rule:

A power law that rank orders a set of objects.

Reaction‐diffusion:

The process of generating changes as a consequence of a reaction to an existing state and interactions between states.

Scale‐free networks:

Networks whose nodal volumes follow a power law.

Segregation model:

A model which generates extreme global segregation from weak assumptions about local segregation.

Simulation:

The process of generating locational distributions according to a series of sub‐model equations or rules.

Slow dynamics:

Changes in the urban system that take place over years or decades.

Social physics:

The application of classical physical principles involving distance, force and mass to social situations, particularly to cities and their transport.

Spatial interaction:

The movement of activities between different locations ranging from traffic distributions to migration patterns.

Trip distribution:

The pattern of movement relating to trips made by the population, usually from home to work but also to other activities such as shopping.

Urban hierarchy:

A set of entities physically or spatially scaled in terms of their size and areal extent.

Urban morphology:

Patterns of urban structure based on the way activities are ordered with respect to their locations.

Urban system:

A city represented as a set of interacting subsystems or their elements.

Bibliography

Primary Literature

  1. Acevedo W, Gaydos L, Tilley J, Mladinich C, Buchanan J, Blauer S, Kruger K, Schubert J (1997) Urban land use change in the Las Vegas valley. US Geological Survey, Washington

    Google Scholar 

  2. Albert R, Jeong H, Barabási A-L (1999) Diameter of the world wide web. Nature 401:130–131

    Google Scholar 

  3. Allen PM (1982) Evolution, modelling, and design in a complex world. Environ Plan B 9:95–111

    Google Scholar 

  4. Allen PM (1998) Cities and regions as self‐organizing systems: models of complexity. Taylor and Francis, London

    Google Scholar 

  5. Alonso W (1964) Location and land use. Harvard University Press, Cambridge

    Google Scholar 

  6. Anas A (1983) Discrete choice theory, information theory and the multinomial logit and gravity models. Transp Res B 17B:13–23

    MathSciNet  Google Scholar 

  7. Andersson C, Rasmussen S, White R (2002) Urban settlements transition. Environ Plan B 29:841–865

    Google Scholar 

  8. Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512

    Google Scholar 

  9. Barredo JI, Kasanko M, McCormick N, Lavalle C (2003) Modeling dynamic spatial processes: simulation of urban future scenarios through cellular automata. Landscape Urban Plan 64:145–160

    Google Scholar 

  10. Batty M (1974) Spatial entropy. Geograph Anal 6:1–31

    Google Scholar 

  11. Batty M (1976) Urban modelling: algorithms, calibration, predictions. Cambridge University Press, Cambridge

    Google Scholar 

  12. Batty M (2005) Agents, cells, and cities: new representational models for simulating multiscale urban dynamics. Environ Plan A 37(8):1373–1394

    Google Scholar 

  13. Batty M (2005) Cities and complexity: understanding cities with cellular automata, agent‐based models, and fractals. MIT Press, Cambridge

    Google Scholar 

  14. Batty M (2006) Rank clocks. Nature 444:592–596

    ADS  Google Scholar 

  15. Batty M (2008) The size, scale, and shape of cities. Science 319(5864):769–771

    ADS  Google Scholar 

  16. Batty M, Longley PA (1994) Fractal cities: a geometry of form and function. Academic Press, San Diego

    Google Scholar 

  17. Batty M, Torrens PM (2005) Modelling and prediction in a complex world. Futures 37(7):745–766

    Google Scholar 

  18. Batty M, Xie Y (1994) From cells to cities. Environ Plan B 21:s31–s48

    Google Scholar 

  19. Batty M, Xie Y, Sun Z (1999) Modeling urban dynamics through GIS‐based cellular automata. Comput Environ Urban Syst 23:205–233

    Google Scholar 

  20. Ben Akiva M, Lerman S (1985) Discrete choice analysis. MIT Press, Cambridge

    Google Scholar 

  21. Berry BJL (1964) Cities as systems within systems of cities. Papers Proc Region Sci Assoc 13:147–164

    ADS  Google Scholar 

  22. Besussi E, Cecchini A, Rinaldi E (1998) The diffused city of the italian north‐east: identification of urban dynamics using cellular automata urban models. Comp Environ Urban Syst 22:497–523

    Google Scholar 

  23. Blank A, Solomon S (2000) Power laws in cities population, financial markets and internet sites: scaling and systems with a variable number of components. Physica A 287:279–288

    MathSciNet  ADS  Google Scholar 

  24. Cardillo A, Scellato S, Latora V, Porta S (2006) Structural properties of planar graphs of urban street patterns. Phys Rev E 73:066107-1–8

    ADS  Google Scholar 

  25. Castle CJE, Crooks AT (2006) Principles and concepts of agent‐based modelling for developing geospatial simulations. Working Paper 110. Centre for Advanced Spatial Analysis, University College London, London

    Google Scholar 

  26. Chadwick GF (1971) A systems view of planning. Pergamon Press, Oxford

    Google Scholar 

  27. Chapin FS, Weiss SF (1968) A probabilistic model for residential growth. Transp Res 2:375–390

    Google Scholar 

  28. Cheng J (2003) Modelling spatial and temporal urban growth. Ph D Thesis, ITC Dissertation 99, ITC, Enschede, Netherlands

    Google Scholar 

  29. Clark C (1951) Urban population densities. J Royal Stat Soc Ser A 114:490–496

    Google Scholar 

  30. Clarke G (ed) (1996) Microsimulation for urban and regional policy analysis. Pion Press, London

    Google Scholar 

  31. Clarke KC, Gaydos LJ (1998) Loose coupling a cellular automaton model and GIS: long‐term growth prediction for San Francisco and Washington/Baltimore. Int J Geograph Inform Sci 12:699–714

    Google Scholar 

  32. Couclelis H (1985) Cellular worlds: a framework for modeling micro‐macro dynamics. Environ Plan A 17:585–596

    Google Scholar 

  33. Crucitti P, Latora V, Porta S (2006) Centrality measures in spatial networks of urban streets. Phys Rev E 73:036125-1-5

    ADS  Google Scholar 

  34. Curry L (1964) The random spatial economy: an exploration in settlement theory. Ann Assoc Amer Geograph 54:138–146

    Google Scholar 

  35. de Almeida CM, Batty M, Câmara G, Cerqueira GC, Monteiro AMV, Pennachin CP, Soares-Filho BS (2003) Stochastic cellular automata modeling of urban land use dynamics: empirical development and estimation. Comput Environ Urban Syst 27:481–509

    Google Scholar 

  36. Dendrinos DS, Mullally H (1985) Urban evolution: studies in the mathematical ecology of cities. Oxford University Press, Oxford

    Google Scholar 

  37. Epstein JM, Axtell RL (1996) Growing artificial societies: social science from the bottom up. MIT Press, Cambridge

    Google Scholar 

  38. Feigenbaum MJ (1980) The metric universal properties of period doubling bifurcations and the spectrum for a route to turbulence. Ann New York Acad Sci 357:330–336

    ADS  Google Scholar 

  39. Forrester JW (1969) Urban dynamics. MIT Press, Cambridge

    Google Scholar 

  40. Fujita M, Krugman P, Venables AJ (1999) The spatial economy: cities, regions, and international trade. MIT Press, Cambridge

    Google Scholar 

  41. Gabaix X (1999) Zipf’s law for cities: an explanation. Quart J Econom 114:739–767

    Google Scholar 

  42. Gell-Man M (1994) The quark and the jaguar: adventures in the simple and the complex. Freeman and Company, New York

    Google Scholar 

  43. Gibrat R (1931) Les inégalités économiques. Librarie du Recueil Sirey, Paris

    Google Scholar 

  44. Gilbert N (2007) Agent‐based models. Sage Inc., Thousand Oaks

    Google Scholar 

  45. Haag G (1989) Dynamic decision theory: applications to urban and regional topics. Kluwer, Dordrecht

    Google Scholar 

  46. Helbing D, Nagel K (2004) The physics of traffic and regional development. Contemp Phys 45:405–426

    ADS  Google Scholar 

  47. Hillier B (1996) Space is the machine. Cambridge University Press, Cambridge

    Google Scholar 

  48. Jiang B (2007) A topological pattern of urban street networks: universality and peculiarity. Physica A 384:647–655

    ADS  Google Scholar 

  49. Lathrop GT, Hamburg JR (1965) An opportunity‐accessibility model for allocating regional growth. J Amer Inst Plan 31:95–103

    Google Scholar 

  50. Lowry IS (1964) Model of metropolis. Memorandum RM-4035-RC. Rand Corporation, Santa Monica

    Google Scholar 

  51. Mandelbot BB (1983) The fractal geometry of nature. Freeman, New York

    Google Scholar 

  52. May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261:459–467

    ADS  Google Scholar 

  53. McLoughlin JB (1969) Urban and regional planning: a systems approach. Faber and Faber, London

    Google Scholar 

  54. Miller JH, Page SE (2007) Complex adaptive systems: an introduction to computational models of social life. Princeton University Press, Princeton

    Google Scholar 

  55. Nagel K, Beckman RJ, Barrett CL (1999) TRANSIMS for urban planning. LA-UR 984389. Los Alamos National Laboratory, Los Alamos

    Google Scholar 

  56. Newman M, Barabási A-L, Watts DJ (2006) The structure and dynamics of networks. Princeton University Press, Princeton

    Google Scholar 

  57. Nijkamp P, Reggiani A (1992) Interaction, evolution and chaos in space. Springer, Berlin

    Google Scholar 

  58. Papini L, Rabino GA, Colonna A, Di Stefano V, Lombardo S (1998) Learning cellular automata in a real world: the case study of the rome metropolitan area. In: Bandini S, Serra R, Suggi Liverani F (eds) Cellular automata: research towards industry: ACRI’96. Proc of the 3rd Conference on cellular automata for research and industry. Springer, London, pp 165–183

    Google Scholar 

  59. Portugali J, Benenson I (1996) Human agents between local and global forces in a self‐organizing city. In: Schweitzer F (ed) Self‐organization of complex structures: from individual to collective dynamics. Gordon and Breach, London, pp 537–545

    Google Scholar 

  60. Propolis (2004) PROPOLIS (policies and research of policies for land use and transport for increasing urban sustainability). Final report for the Commission of the European Communities. LT Consultants Ltd, Helsinki

    Google Scholar 

  61. Schelling TC (1969) Models of segregation. Amer Econom Rev Papers Proc 58(2):488–493

    Google Scholar 

  62. Schelling TC (1978) Micromotives and macrobehavior. Norton and Company, New York

    Google Scholar 

  63. Schweitzer F, Steinbrink J (1997) urban cluster growth: analysis and computer simulation of urban aggregations. In: Schweitzer F (ed) Self‐organization of complex structures: from individual to collective dynamics. Gordon and Breach, London, pp 501–518

    Google Scholar 

  64. Semboloni F (2000) The growth of an urban cluster into a dynamic self‐modifying spatial pattern. Environ Plan B 27:549–564

    Google Scholar 

  65. Tobler WR (1970) A computer movie simulating population growth in the detroit region. Econom Geograph 42:234–240

    Google Scholar 

  66. Tribus M (1969) Rational, descriptions, decisions and designs. Pergamon Press, New York

    Google Scholar 

  67. von Bertalanffy L (1969) General system theory: foundations, development, applications. George Braziller, New York. Revised Edition (1976)

    Google Scholar 

  68. von Thünen JH (1826) Von Thunen’s isolated state. Pergamon, Oxford. (1966 translation from the 1826 German Edition Der isolierte Staat in Beziehung auf Landwirtschaft und Nationaloekonomie by P. G. Hall)

    Google Scholar 

  69. Waddell P (2002) UrbanSim: modeling urban development for land use, transportation and environmental planning. J Amer Plan Assoc 68:297–314

    Google Scholar 

  70. Ward DP, Murray AT, Phinn SR (2000) A stochastically constrained cellular model of urban growth. Comput Environ Urban Syst 24:539–558

    Google Scholar 

  71. Wegener M (2005) Urban land‐use transportation models. In: Maguire DJ, Batty M, Goodchild MF (eds) GIS, spatial analysis, and modeling. ESRI Press, Redlands, pp 203–220

    Google Scholar 

  72. White RW, Engelen G (1993) Cellular automata and fractal urban form: a cellular modelling approach to the evolution of urban land use patterns. Environ Plan A 25:1175–1193

    Google Scholar 

  73. Wiener N (1965) Cybernetics: or the control and communication in the animal and the machine, 2nd edn. MIT Press, Cambridge

    Google Scholar 

  74. Wilson AG (1970) Entropy in urban and regional modelling. Pion Press, London

    Google Scholar 

  75. Wilson AG (1981) Catastrophe theory and bifurcation; applications to urban and regional systems. University of California Press, Berkeley

    Google Scholar 

  76. Wilson AG (2007) Boltzmann, Lotka, and Volterra and spatial structural evolution: a integrated methodology for some dynamical systems. J Royal Soc Interface 1–7. doi:10.1098/rsif.2007.1288

  77. Wu F, Webster CJ (1998) Simulation of land development through the integration of cellular automata and multicriteria evaluation. Environ Plan B 25:103–126

    Google Scholar 

  78. Xie Y (1994) Analytical models and algorithms for cellular urban dynamics. Unpublished Ph D dissertation, State University of New York at Buffalo, Buffalo

    Google Scholar 

  79. Xie Y, Batty M (2005) Integrated urban evolutionary modeling. In: Atkinson PM, Foody GM, Darby SE, Wu F (eds) Geodynamics. CRC Press, Boca Raton, pp 273–293

    Google Scholar 

  80. Yeh A G-O, Li X (2000) A ‘Grey‐Cell’ constrained ca model for the simulation of urban forms and developments in the planning of sustainable cities using GIS. Centre of Urban Planning and Environmental Management. University of Hong Kong, Pokfulam

    Google Scholar 

  81. Zipf GK (1949) Human behavior and the principle of least effort. Addison-Wesley, Cambridge

    Google Scholar 

Books and Reviews

  1. Barabási A (2002) Linked: the new science of networks. Perseus Publishing, New York

    Google Scholar 

  2. Batty M, Couclelis H, Eichen M (1997) Urban systems as cellular automata. Environ Plan B 24:159–164

    Google Scholar 

  3. Benenson I, Torrens PM (2004) Geosimulation: automata‐based modeling of urban phenomena. Wiley, London

    Google Scholar 

  4. Clarke M, Wilson AG (1993) Dynamics of urban spatial structure: progress and problems. J Region Sci 21:1–18

    Google Scholar 

  5. Couclelis H (1997) From cellular automata models to urban models: new principles for model development and implementation. Environ Plan B 24:165–174

    Google Scholar 

  6. Dendrinos DS, Sonis M (1990) Chaos and socio‐spatial dynamics. Springer, New York

    Google Scholar 

  7. Haggett P, Chorley R (1969) Network analysis in geography. Edward Arnold, London

    Google Scholar 

  8. Helbing D, Molnar P Farkas IJ, Bolay K (2001) Self‐organizing pedestrian movement. Environ Plan B 28:361–383

    Google Scholar 

  9. Holland JH (1995) Hidden order: how adaptation builds complexity. Addison-Wesley, Reading

    Google Scholar 

  10. Isard W (1956) Location and space‐economy: a general theory relating to industrial location, market areas, land use, trade and urban structure. MIT Press, Cambridge

    Google Scholar 

  11. Jacobs J (1961) The death and life of great american cities. Vintage Books, Random House

    Google Scholar 

  12. Krugman PR (1996) The self‐organizing economy. Blackwell, Cambridge

    Google Scholar 

  13. Portugali J (2000) Self‐organization and the city. Springer, Berlin

    Google Scholar 

  14. Resnick M (1994) Termites, turtles and traffic jams: explorations in massively parallel micro‐worlds. MIT Press, Cambridge

    Google Scholar 

  15. Sanders L, Pumain D, Mathian H, Guerin-Pace F, Bura S (1997) SIMPOP: a multiagent system for the study of urbanism. Environ Plan B 24:287–305

    Google Scholar 

  16. Simon HA (1969, 1996) Sciences of the artificial. MIT Press, Cambridge

    Google Scholar 

  17. Stewart JQ, Warntz W (1958) Physics of population distribution. J Region Sci 1:99–123

    Google Scholar 

  18. White RW (1998) Cities and cellular automata. Discrete Dyn Nature Soc 2:111–125

    Google Scholar 

  19. Willumsen LG, de Ortuzar JD (1990) Modelling transport. Wiley, Chichester

    Google Scholar 

  20. Wilson AG (2000) Complex spatial systems: the modelling foundations of urban and regional analysis. Pearson Education, Harlow

    Google Scholar 

  21. Wilson AG (1974) Urban and regional models in geography and planning. Wiley, Chichester

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Advanced Spatial Analysis, University College London, London, UK

    Michael Batty

Authors
  1. Michael Batty
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag

About this entry

Cite this entry

Batty, M. (2009). Cities as Complex Systems: Scaling, Interaction, Networks, Dynamics and Urban Morphologies. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_69

Download citation

Publish with us

Policies and ethics

Search

Navigation