From raster to vector cellular automata models: A new approach to simulate urban growth with the help of graph theory

Abstract The majority of celullar automata (CA) based models developed to simulate land use changes or urban growth employed a raster representation of the space which reduces reality into regular pieces. This approach is perfectly valid when simulating on large study areas. However, the use of vector representation of space becomes more useful in small extensions since they represent land use covers in a more realistic way. In this regard, a new vector CA-based prototype is presented making use of cadastral parcels and cellular space is combined with graph theory to get a better operability. Neighbourhood factors are defined more flexibly since every parcel is different from the rest. Accessibility, suitability and zoning were computed and added to the prototype's transition rules. A little municipality within the Community of Madrid, one of the most dynamic spaces in terms of urban growth over the last decades, was selected to test the prototype.

[1]  Xinhao Wang,et al.  A cellular automata model of land cover change to integrate urban growth with open space conservation , 2011 .

[2]  Juval Portugali,et al.  Self-Organization and the City , 2009, Encyclopedia of Complexity and Systems Science.

[3]  B. De Baets,et al.  Effect of asynchronous updating on the stability of cellular automata , 2012 .

[4]  Suzana Dragicevic,et al.  iCity: A GIS-CA modelling tool for urban planning and decision making , 2007, Environ. Model. Softw..

[5]  Joaquín Bosque Sendra,et al.  Cambios de usos del suelo y expansión urbana en la Comunidad de Madrid (1990-2000) , 2009 .

[6]  F. Peper,et al.  Asynchronous game of life , 2004 .

[7]  José I. Barredo,et al.  Modelling Future Urban Scenarios in Developing Countries: An Application Case Study in Lagos, Nigeria , 2004 .

[8]  F. Aguilera,et al.  Landscape metrics in the analysis of urban land use patterns: A case study in a Spanish metropolitan area , 2011 .

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

[10]  T. Edwin Chow,et al.  An agent-integrated irregular automata model of urban land-use dynamics , 2014, Int. J. Geogr. Inf. Sci..

[11]  Pierre Frankhauser,et al.  Fractal geometry of urban patterns and their morphogenesis , 1998 .

[12]  Paul Schot,et al.  Land use change modelling: current practice and research priorities , 2004 .

[13]  P. Torrens,et al.  Geosimulation: Automata-based modeling of urban phenomena , 2004 .

[14]  G Engelen,et al.  Using cellular automata for integrated modelling of socio-environmental systems , 1995, Environmental monitoring and assessment.

[15]  Suzana Dragicevic,et al.  Modeling urban growth using a variable grid cellular automaton , 2009, Comput. Environ. Urban Syst..

[16]  Paul M. Torrens,et al.  Cellular Models of Urban Systems , 2000, ACRI.

[17]  Jianguo Wu,et al.  Modeling urban landscape dynamics: A review , 2004, Ecological Research.

[18]  A. Antunes,et al.  A Cellular Automata Model Based on Irregular Cells: Application to Small Urban Areas , 2010 .

[19]  Jamal Jokar Arsanjani,et al.  ntegration of logistic regression , Markov chain and cellular automata odels to simulate urban expansion amal , 2012 .

[20]  Fang Wang,et al.  Implementation of a dynamic neighborhood in a land-use vector-based cellular automata model , 2009, Comput. Environ. Urban Syst..

[21]  Scott J. Goetz,et al.  Designing and implementing a regional urban modeling system using the SLEUTH cellular urban model , 2010, Comput. Environ. Urban Syst..

[22]  A. Turing On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[23]  Claes Andersson,et al.  Assessing the impact of temporal dynamics on land-use change modeling , 2004, Comput. Environ. Urban Syst..

[24]  Michael Batty,et al.  Urban Evolution on the Desktop: Simulation with the Use of Extended Cellular Automata , 1998 .

[25]  Suzana Dragicevic,et al.  Assessing cellular automata model behaviour using a sensitivity analysis approach , 2006, Comput. Environ. Urban Syst..

[26]  L. Deren,et al.  VECTOR CELLULAR AUTOMATA BASED GEOGRAPHICAL ENTITY , 2004 .

[27]  Elisabete A. Silva,et al.  Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal , 2002 .

[28]  Noah Goldstein,et al.  Brains Vs. Brawn – Comparative Strategies For The Calibration Of A Cellular Automata – Based Urban Growth Model , 2003 .

[29]  I. Bishop,et al.  Simulating urban growth in a developing nation's region using a cellular automata-based model , 2004 .

[30]  Michael Batty,et al.  Cities and complexity - understanding cities with cellular automata, agent-based models, and fractals , 2007 .

[31]  W. Tobler A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[32]  Francisco Escobar,et al.  Participatory land use modelling, pathways to an integrated approach , 2014, Environ. Model. Softw..

[33]  David G. Green,et al.  Ordered asynchronous processes in multi-agent systems , 2005 .

[34]  M. Batty,et al.  Modeling urban dynamics through GIS-based cellular automata , 1999 .

[35]  Danielle J. Marceau,et al.  VecGCA: A Vector-Based Geographic Cellular Automata Model Allowing Geometric Transformations of Objects , 2008 .

[36]  Alexander Moffett,et al.  A Dynamic Graph Automata Approach to Modeling Landscape Change in the Andes and the Amazon , 2009 .

[37]  Helen Couclelis,et al.  Cellular Worlds: A Framework for Modeling Micro—Macro Dynamics , 1985 .

[38]  José I. Barredo,et al.  The MOLAND Modelling Framework for Urban and Regional Land Use Dynamics , 2007 .

[39]  J. Anez,et al.  Dual graph representation of transport networks , 1996 .

[40]  Guido Van Rossum,et al.  Python Tutorial , 1999 .

[41]  Yan Liu,et al.  Modelling sustainable urban growth in a rapidly urbanising region using a fuzzy-constrained cellular automata approach , 2012, Int. J. Geogr. Inf. Sci..

[42]  Khila R. Dahal,et al.  Characterization of neighborhood sensitivity of an irregular cellular automata model of urban growth , 2015, Int. J. Geogr. Inf. Sci..

[43]  Scott J. Goetz,et al.  Analysis of scale dependencies in an urban land‐use‐change model , 2005, Int. J. Geogr. Inf. Sci..

[44]  Wenzhong Shi,et al.  Development of Voronoi-based cellular automata -an integrated dynamic model for Geographical Information Systems , 2000, Int. J. Geogr. Inf. Sci..

[45]  B. Schönfisch,et al.  Synchronous and asynchronous updating in cellular automata. , 1999, Bio Systems.

[46]  Ferdinando Semboloni,et al.  The Growth of an Urban Cluster into a Dynamic Self-Modifying Spatial Pattern , 2000 .

[47]  P. Torrens,et al.  Cellular Automata and Urban Simulation: Where Do We Go from Here? , 2001 .

[48]  Aric Hagberg,et al.  Exploring Network Structure, Dynamics, and Function using NetworkX , 2008, Proceedings of the Python in Science Conference.

[49]  Luis Miguel Valenzuela Montes,et al.  Simulación de escenarios futuros en la aglomeración urbana de Granada a través de modelos basados en autómatas celulares , 2010 .

[50]  Stephen Wolfram,et al.  Cellular automata as models of complexity , 1984, Nature.

[51]  José I. Barredo,et al.  Are European Cities Becoming Dispersed? A Comparative Analysis of 15 European Urban Areas , 2006 .

[52]  Suzana Dragicevic,et al.  A GIS-Based Irregular Cellular Automata Model of Land-Use Change , 2007 .

[53]  Danielle J. Marceau,et al.  Exploration of Spatial Scale Sensitivity in Geographic Cellular Automata , 2005 .

[54]  Andrew V. Goldberg,et al.  Computing the shortest path: A search meets graph theory , 2005, SODA '05.

[55]  R. White,et al.  High-resolution integrated modelling of the spatial dynamics of urban and regional systems , 2000 .

[56]  Andrés Manuel García,et al.  Cellular automata models for the simulation of real-world urban processes: A review and analysis , 2010 .

[57]  Ren-qing Wang,et al.  Incorporating spatial autocorrelation into cellular automata model: An application to the dynamics of Chinese tamarisk (Tamarix chinensis Lour.) , 2009 .

[58]  Robert M. Itami,et al.  Simulating spatial dynamics: cellular automata theory , 1994 .

[59]  Patrick Hostert,et al.  Uncovering land-use dynamics driven by human decision-making - A combined model approach using cellular automata and system dynamics , 2012, Environ. Model. Softw..

[60]  Andrés Manuel García,et al.  An analysis of the effect of the stochastic component of urban cellular automata models , 2011, Comput. Environ. Urban Syst..

[61]  Xia Li,et al.  Discovering and evaluating urban signatures for simulating compact development using cellular automata , 2008 .

[62]  C. Lavalle,et al.  Modelling dynamic spatial processes: simulation of urban future scenarios through cellular automata , 2003 .

[63]  M. Batty,et al.  Stochastic cellular automata modeling of urban land use dynamics: empirical development and estimation , 2003, Comput. Environ. Urban Syst..

[64]  Narimah Samat,et al.  Characterizing the scale sensitivity of the cellular automata simulated urban growth: A case study of the Seberang Perai Region, Penang State, Malaysia , 2006, Comput. Environ. Urban Syst..

[65]  Hedwig van Delden,et al.  Measuring the neighbourhood effect to calibrate land use models , 2013, Comput. Environ. Urban Syst..

[66]  Fulong Wu,et al.  Calibration of stochastic cellular automata: the application to rural-urban land conversions , 2002, Int. J. Geogr. Inf. Sci..

[67]  Roger White,et al.  Cellular Automata and Fractal Urban Form: A Cellular Modelling Approach to the Evolution of Urban Land-Use Patterns , 1993 .

[68]  Roger White,et al.  The Use of Constrained Cellular Automata for High-Resolution Modelling of Urban Land-Use Dynamics , 1997 .

[69]  Montserrat Gómez Delgado Análisis de la dinámica urbana y simulación de escenarios de desarrollo futuro con tecnologías de la información geográfica , 2012 .

[70]  M. Helbich,et al.  Spatiotemporal urbanization processes in the megacity of Mumbai, India: A Markov chains-cellular automata urban growth model , 2013 .

[71]  Keith C. Clarke,et al.  Spatial Differences in Multi‐Resolution Urban Automata Modeling , 2004, Trans. GIS.

[72]  K. Seto,et al.  A Meta-Analysis of Global Urban Land Expansion , 2011, PloS one.

[73]  G. Mountrakis,et al.  Urban Growth Prediction: A Review of Computational Models and Human Perceptions , 2012 .

[74]  Sally Macgill Research Policy and Review 12. Evaluating a Heritage of Modelling Styles , 1986 .

[75]  Qian Zhang,et al.  Simulation and analysis of urban growth scenarios for the Greater Shanghai Area, China , 2011, Comput. Environ. Urban Syst..

[76]  Qinglan Xia OPTIMAL PATHS RELATED TO TRANSPORT PROBLEMS , 2003 .

[77]  Helen Couclelis,et al.  From Cellular Automata to Urban Models: New Principles for Model Development and Implementation , 1997 .

[78]  Chris S. Renschler,et al.  A formal model to infer geographic events from sensor observations , 2015, Int. J. Geogr. Inf. Sci..

[79]  Mark Brussel,et al.  A cellular automata-based land use and transport interaction model applied to Jeddah, Saudi Arabia , 2013 .

[80]  M. Gómez,et al.  Towards a set of IPCC SRES urban land use scenarios: modelling urban land use in the Madrid region , 2008 .

[81]  David O'Sullivan,et al.  Exploring Spatial Process Dynamics Using Irregular Cellular Automaton Models , 2010 .

[82]  David O'Sullivan Graph-Cellular Automata: A Generalised Discrete Urban and Regional Model , 2001 .

[83]  Pablo Barreira González,et al.  Partial validation of cellular automata based model simulations of urban growth: An approach to assessing factor influence using spatial methods , 2015, Environ. Model. Softw..

[84]  Roger White,et al.  Cities and cellular automata , 1998 .

[85]  Enrique Bardají Alvarez El planeamiento de escala intermedia como corazón del planeamiento español: Una propuesta de nueva organización de las figuras de planeamiento , 2011 .

[86]  M. Alberti,et al.  Ecological resilience in urban ecosystems: Linking urban patterns to human and ecological functions , 2004, Urban Ecosystems.