Space–Time Patterns of Urban Sprawl, a 1D Cellular Automata and Microeconomic Approach

We present a theoretical model of residential growth that emphasises the path-dependent nature of urban sprawl patterns. The model is founded on the monocentric urban economic model and uses a cellular automata (CA) approach to introduce endogenous neighbourhood effects. Households are assumed both to like and to dislike the density of their neighbourhood, and are assumed to trade-off this density with housing space consumption and commuting costs. Discontinuous spatial patterns emerge from that trade-off, with the size of suburban clusters varying with time and distance to the centre. We use space–time diagrams inspired from 1D elementary CA to visualise changes in spatial patterns through time and space, and undertake sensitivity analyses to show how the pattern and timing of sprawl are affected by neighbourhood preferences, income level, commuting costs, or by imposing a green belt.

[1]  T. Schelling.  Models of Segregation , 1969 .

[2]  Everett M. Rogers,et al.  Innovation Diffusion As a Spatial Process , 1967 .

[3]  Thomas C. Schelling,et al.  Dynamic models of segregation , 1971 .

[4]  W. Hamilton,et al.  The evolution of cooperation. , 1984, Science.

[5]  Stephen Wolfram,et al.  Universality and complexity in cellular automata , 1983 .

[6]  A. Nelson.  A Unifying View of Greenbelt Influences on Regional Land Values and Implications for Regional Planning Policy , 1985 .

[7]  Takahiro Miyao,et al.  Dynamic urban models , 1987 .

[8]  Jeffrey Kenworthy,et al.  Gasoline Consumption and Cities: A Comparison of U.S. Cities with a Global Survey , 1989 .

[9]  Y. Kanemoto,et al.  Urban Dynamics and Urban Externalities , 1987 .

[10]  Harry W. Richardson,et al.  GASOLINE CONSUMPTION AND CITIES: A REPLY , 1989 .

[11]  藤田 昌久,et al.  Urban economic theory : land use and city size , 1989 .

[12]  Alan W. Evans,et al.  'Rabbit Hutches on Postage Stamps': Planning, Development and Political Economy , 1991 .

[13]  Christopher G. Langton,et al.  Life at the Edge of Chaos , 1992 .

[14]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[15]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[16]  E. Mills,et al.  The Causes of Metropolitan Suburbanization , 1993 .

[17]  Location and History as Determinants of Urban Residential Density , 1995 .

[18]  Paul Cheshire,et al.  On the Price of Land and the Value of Amenities , 1995 .

[19]  M. Breheny.  The compact city and transport energy consumption , 1995 .

[20]  M. Fukui,et al.  Traffic Flow in 1D Cellular Automaton Model Including Cars Moving with High Speed , 1996 .

[21]  M. Fujita,et al.  Efficient Configuration of a Greenbelt: Theoretical Modelling of Greenbelt Amenity , 1997 .

[22]  Peter Hall,et al.  The Future of the Metropolis and its Form , 1997 .

[23]  Keith C. Clarke,et al.  A Self-Modifying Cellular Automaton Model of Historical Urbanization in the San Francisco Bay Area , 1997 .

[24]  Guy Engelen,et al.  Cellular Automata as the Basis of Integrated Dynamic Regional Modelling , 1997 .

[25]  Michael Batty,et al.  Urban Systems as Cellular Automata , 1997 .

[26]  Martin A. Nowak,et al.  Games on Grids , 1999 .

[27]  Jeffrey D. Kline,et al.  Does Land Use Planning Slow the Conversion of Forest and FarmLands , 1999 .

[28]  R. Lilieholm,et al.  The Economic Value of Open Space: A Review and Synthesis , 1999, Environmental management.

[29]  J. Brueckner.  Urban Sprawl: Diagnosis and Remedies , 2000 .

[30]  Noelwah R. Netusil,et al.  The impact of open spaces on property values in Portland, Oregon , 2000 .

[31]  Elena G. Irwin,et al.  The Effects of Open Space on Residential Property Values , 2002, Land Economics.

[32]  J. Geoghegan.  The value of open spaces in residential land use , 2002 .

[33]  Lori Lynch,et al.  Capitalization of Open Spaces into Housing Values and the Residential Property Tax Revenue Impacts of Agricultural Easement Programs , 2003, Agricultural and Resource Economics Review.

[34]  Andrew J. Plantinga,et al.  The influence of public open space on urban spatial structure , 2003 .

[35]  S. Lai.  On transition rules of complex structures in one-dimensional cellular automata: Some implicaltions for urban change , 2003 .

[36]  William Rand,et al.  Agent-based and analytical modeling to evaluate the effectiveness of greenbelts , 2004, Environ. Model. Softw..

[37]  Dawn C. Parker,et al.  Measuring pattern outcomes in an agent-based model of edge-effect externalities using spatial metrics , 2004 .

[38]  Dominique Peeters,et al.  The periurban city: why to live between the suburbs and the countryside , 2004 .

[39]  Paul M. Torrens,et al.  Geosimulation: Object-based Modeling of Urban Phenomena , 2022 .

[40]  Dominique Peeters,et al.  Where Alonso Meets Sierpinski: An Urban Economic Model of a Fractal Metropolitan Area , 2004 .

[41]  Mark Rounsevell,et al.  Exploring a spatio‐dynamic neighbourhood‐based model of residential behaviour in the Brussels periurban area , 2005, Int. J. Geogr. Inf. Sci..

[42]  M. Turner.  Landscape preferences and patterns of residential development , 2005 .

[43]  K. Doi,et al.  Multiagent Land-Use and Transport Model for the Policy Evaluation of a Compact City , 2005 .

[44]  François-Pierre Tourneux,et al.  Seeing and being seen : a GIS-based hedonic price valuation of landscape , 2006 .

[45]  Soren T. Anderson,et al.  Open Space, Residential Property Values, and Spatial Context , 2006 .

[46]  Dominique Peeters,et al.  Spatial configurations in a periurban city. A cellular automata-based microeconomic model , 2007 .

[47]  Laurence A. Wolsey,et al.  Two row mixed-integer cuts via lifting , 2010, Math. Program..