A cellular automata model to simulate development

1IntroductionCellularautomata(CA)werefirstintroducedin1948byvonNeumannandUlamtomodelcomplexdynamicsystems,suchasbiologicalreproductionandcrystalgrowth(Goles,1989).The`gameoflife'developedin1970bythemathematicianConwaycanberegardedasanexplicitCAgame(Gardner,1971;Portugali,2000).AlthoughCAmodelsuseonlyverysimplerules,theycangenerateverycomplexbehaviorandglobalstructures.Theyhavegreatpotentialinsimulatingurbangrowthandexploringalternativedevelop-mentformssubjecttopredefinedrules.ManystudiesonurbanCAmodelswithinterestingoutcomeshavebeenreported(BattyandXie,1994;1997;Couclelis,1997;Deadmanetal,1993;LiandYeh,2000;WhiteandEngelen,1997;WuandWebster,1998).CAmodelscanprovideproceduresforthedesignofoptimalforms(Batty,1997).Theymaybecomepowerfulplanningtoolswhenintegratedwithgeographicalinfor-mationsystems(GIS),whichcansupplyphysical,social,andeconomicdataforthesimulation.RecentCAmodelshavegenerallybeenlinkedtoGISbyusinganinhomogeneousarrayofcellssothatthetransitionrulesare,inasense,sitespecific.RemotesensingandGISareintegratedwithCAinprovidingdetailedland-useinformationaswellasinformationonothercharacteristicsofcitiestoallowrealisticurbansimulation(LiandYeh,2000).Recently,attemptshavebeenmadetodevelopakindofCAmodelthatcanbeusedasamodelforurbanplanning(LiandYeh,2000;2001;Wardetal,2000;YehandLi,2001a).WehaveusedconstrainedCAandGIStoplanforsustainableurbandevelopmentaimingatminimizingagriculturallandlossandpromotingcompactdevelopment(LiandYeh,2000).Variousurbanformsassociatedwithdifferentdevelopmentandenergy`costs'canalsobeexploredbyusingconstrainedCAmodelsfortestingdifferentplanningoptions(YehandLi,2001a).Wardetal(2000)havealsodevelopedaconstrainedCAAcellularautomatamodeltosimulatedevelopmentdensityforurbanplanningAnthonyGar-OnYeh,XiaLi}CentreofUrbanPlanningandEnvironmentalManagement,UniversityofHongKong,PokfulamRoad,HongKongSAR,People'sRepublicofChina;e-mail:[e-mail],[e-mail]12February2001;inrevisedform5September2001EnvironmentandPlanningB:PlanningandDesign2002,volume29,pages431^450Abstract.Mostcellularautomata(CA)urbanmodelsassumedensitiestobeuniformforallcells.Thisisnottrueinrealcitiesbecausedensitiesvarysubstantiallyfromcitytocityandfromurbancentertoperipheryareas.Developmentdensity,whichaffectsurbanform,isanimportantfactorinurbanplanning.TheauthorspresentaCAmodelthatincorporatesdensitygradientinthesimulationofurbandevelopmentfordifferenturbanforms.Developmentdensityisobtainedfromdensity-decayfunctionsandassignedtothecellswhentheyareconvertedintodevelopedcellsaccordingtoCAtransitionrules.Themodel,whichisbasedontheconceptof`greycells',canbeusedasaplanningmodeltoexplorevariouscombinationsofurbanformsanddevelopmentdensities.Theauthorsalsoevaluateandcomparethedevelopmentpatternsgeneratedbydifferentdensitygradients.Itisfoundthatdevelopmentscenarioswithhigh-densitydevelopmentcansignificantlyreduceencroachmentonagriculturallandandotherimportantenvironmentallysensitiveareas.DOI:10.1068/b1288}AlsoatGuangzhouInstituteofGeography,Guangzhou,People'sRepublicofChina;e-mail:[e-mail]oanareaintheGoldCoast,arapidlyurbanizingregionofcoastaleasternAustralia.TheydemonstratedthatCAmodelscansimulateplanneddevelopmentaswellasrealisticdevelopmentbyincorporatingsustainabilityinthesimulation.Theyshowedthateconomic,physical,andinstitutionalcontrolfactorscanbeincorporatedtomodify,constrain,andprohibiturbangrowth.OneofthemajordrawbacksinexistingurbanCAmodelsisthatmostofthemdonotconsiderdevelopmentdensity,assumingittobeuniformforallcells.However,thedensityissueisveryimportantforurbanplanning,especiallygiventherecentconcernsoversustainabledevelopmentanddebatesoncompactdevelopment.Furthermore,inrealcities,developmentandpopulationdensitiesarenotuniform.Anurbanpopulationdensitygradientexistsinmostcities(Clark,1951;Papageorgiou,1971;Thrall,1988).Thereisalsospatialvariationinlandvalues,resultinginspatialvariationindevelopmentdensityinmonocentriccities(Alonso,1964)andpolycentriccities(Heikkilaetal,1989).OurmainobjectiveinthispaperistopresentaCAmodelthatintegratesadensitygradientforthesimulationofurbandevelopmentofdifferenturbanformsthatcanbeusedasaplanningmodeltoexplorevariouscombinationsofurbanformsanddevelop-mentdensitiestoguidefutureurbandevelopment.Wewillalsoevaluateandcomparethedevelopmentpatternsofdifferentdensitygradientsgeneratedbythemodel.2Developmentdensityandland-useplanningCompactdevelopmentisconsideredtobethemostsuitableurbanformbecauseitcansignificantlyreducetheconsumptionofenergyandlandresources(Ewing,1997).Compactdevelopmentusuallyconcernsthecontiguityorclusteringoflanddevelop-ment.Theconcentrationofdevelopmentisrelatedtotheissueofurbanmorphology,whichhasbeendiscussedelsewhere(seeBrookes,1997;Webster,1995;YehandLi,2001b).Urbanplannersandresearchersareconcernedwiththechangeinshape,size,andconfigurationofthebuiltenvironment.Banisteretal(1997)foundthattherearesignifi-cantrelationshipsbetweenenergyuseintransportandthephysicalcharacteristicsofacity,suchasdensity,size,andamoun