Table Of ContentSpatial Simulation
Spatial Simulation
Exploring Pattern and Process
David O’Sullivan and George L. W. Perry
University of Auckland – Te Whare Wa¯nanga o Ta¯maki Makaurau,
New Zealand
A John Wiley & Sons, Ltd., Publication
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O’Sullivan,David,1966–
Spatialsimulation:exploringpatternandprocess/DavidO’Sullivan,GeorgeL.W.Perry.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-119-97080-4(cloth)–ISBN978-1-119-97079-8(paper)
1.Spatialdatainfrastructures–Mathematicalmodels.2.Spatialanalysis(Statistics)I.Perry,
GeorgeL.W.II.Title.
QA402.O7972013
003–dc23
2012043887
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FirstImpression2013
To
Fintan & Malachy
and
Leo & Ash
Contents
Foreword xiii
Preface xv
Acknowledgements xix
Introduction xxi
About the Companion Website xxv
1 Spatial Simulation Models: What? Why? How? 1
1.1 Whataresimulationmodels? 2
1.1.1 Conceptualmodels 4
1.1.2 Physicalmodels 7
1.1.3 Mathematicalmodels 7
1.1.4 Empiricalmodels 8
1.1.5 Simulationmodels 9
1.2 Howdoweusesimulationmodels? 12
1.2.1 Usingmodelsforprediction 13
1.2.2 Modelsasguidestodatacollection 13
1.2.3 Modelsas‘toolstothinkwith’ 14
1.3 Whydoweusesimulationmodels? 15
1.3.1 Whenexperimentalscienceisdifficult(orimpossible) 16
1.3.2 Complexityandnonlineardynamics 18
1.4 Whydynamicandspatialmodels? 23
1.4.1 Thestrengthsandweaknessesofhighlygeneralmodels 23
1.4.2 Fromabstracttomorerealisticmodels:controllingthecost 27
2 Pattern, Process and Scale 29
2.1 Thinkingaboutspatiotemporalpatternsandprocesses 30
2.1.1 Whatisapattern? 30
viii CONTENTS
2.1.2 Whatisaprocess? 31
2.1.3 Scale 32
2.2 Usingmodelstoexplorespatialpatternsandprocesses 38
2.2.1 Reciprocallinksbetweenpatternandprocess:aspatialmodelof
foreststructure 39
2.2.2 Characterisingpatterns:first-andsecond-orderstructure 40
2.2.3 Usingnullmodelstoevaluatepatterns 43
2.2.4 Density-based(first-order)nullmodels 46
2.2.5 Interaction-based(second-order)nullmodels 48
2.2.6 Inferringprocessfrom(spatio-temporal)pattern 49
2.2.7 Makingthevirtualforestmorerealistic 53
2.3 Conclusions 56
3 Aggregation and Segregation 57
3.1 Backgroundandmotivatingexamples 58
3.1.1 Basicsof(discretespatial)modelstructure 59
3.2 Localaveraging 60
3.2.1 Localaveragingwithnoise 63
3.3 Totalisticautomata 64
3.3.1 Majorityrules 65
3.3.2 Twistedmajorityannealing 68
3.3.3 Life-likerules 69
3.4 Amoregeneralframework:interactingparticlesystems 70
3.4.1 Thecontactprocess 71
3.4.2 Multiplecontactprocesses 73
3.4.3 Cyclicrelationshipsbetweenstates:rock–scissors–paper 76
3.4.4 Votermodels 78
3.4.5 Votermodelswithnoisemutation 80
3.5 Schellingmodels 83
3.6 Spatialpartitioning 86
3.6.1 Iterativesubdivision 86
3.6.2 Voronoitessellations 87
3.7 Applyingtheseideas:morecomplicatedmodels 88
3.7.1 Patternformationonanimals’coats:reaction–diffusionmodels 89
3.7.2 Morecomplicatedprocesses:spatialevolutionarygametheory 91
3.7.3 Morerealisticmodels:cellularurbanmodels 93
4 Random Walks and Mobile Entities 97
4.1 Backgroundandmotivatingexamples 97
4.2 Therandomwalk 99
4.2.1 Simplerandomwalks 99
4.2.2 Randomwalkswithvariablesteplengths 102
4.2.3 Correlatedwalks 103
4.2.4 Biasanddriftinrandomwalks 108
4.2.5 Le´vyflights:walkswithnon-finitesteplengthvariance 109
