交通网络空间结构的分形维数及其测算方法探讨

:1998-01-10;:1999-05-11:(49771035),(974071200)[Foundationitem:NationalNaturalScienceFoundationofChina,No.49771035;NaturalScienceFoundationofHenanProvince,No.974071200]:(1955-),,,,3,40:0375-5444(1999)05-0471-08刘继生1,陈彦光2(1.,130024;2.,464000):,:-,,;-,,;,(),:;;:F511.99:A,(fractalgeometry)(self-similar)[1,2]S.ThibaultA.Marchand(1987)Lyons,N(L)L[3]L.BenguiguiM.Daoud(1991)Paris,,(Diffusion-limitedAggregation,DLA)[4]P.Frankhouser(1990)Stuttgart,r,L(r)r[5],,(fractaldimension),--,,,54519999ACTAGEOGRAPHICASINICAVol.54,No.5Sept.,19991:1.1-,L1/1S1/2V1/3M1/d(1-1)L,S,V,M,LSV,dM=L,d=1,,d,dDS,,(1-1),L(S)L(S)1/DS1/2(1-2),Sr2,(1-2)L(r)=L1rDL(1-3)r,L(r)r,L1,DL,,-,Frankhouser(1991)(radialdimension),(1-3)Stuttgart(1988),D1.581-Fig.1Theln-lnplotonthelengthsofthecommunicationlinesaroundGuangshantownagainstradialdistances1.2(),DL,(1-3),Q(r)rDL-d,d=2:DL2,()DL=2,DL2,,,DL,(1-3)L1,,,W=2lnL/lnS(1-4):(1-4),472541.3Frankhouser,:,r,Pr2L(r)r,L(r),(r,L(r)),,(non-scalingrange),,,,r,L(r),(r,L(r))(1),(1),DL=1.750,R2=0.9831XTab.1Radialdistances(r)andthetotallengths(L(r))ofcommunicationlinesaroundthetownofGuangshanr/5mm12345678910L(r)/km27.562100.524338055167979110531244.5X1.:¹(),,1994;º,,1996(:150)2.2:2.1-,,,,,,,,N(r)rDb(2-1)N(r)=6rk=1n(k)(2-2)r,r,(),k,n(k)kr=1,2,,k=1,2,,r,rk,N(r)Pr2(2-1)N1,N(r)=N1rDb,Db,,()2.2,,;,,(2-1)Q(r)rDb-d,d=2Db,4735:2-Fig.2Theln-lnplotonthenumbersofbranchesoftransportnetworkaroundZhengzhouagainstradialdistances,(2-1)N1Db,,,:,,,,,d=1,,2.3,r,r,,n(k)(:,,n(k)),N(r)(2)(r,N(r)),(2)Db=1.676,R2=0.9992XTab.2Theaccumulatednumbers(N(r))ofbranchesoftransportnetworkaroundthecityofZhengzhouagainstcorrespondingradialdistances(r)k1234567n()7212543495964n()54557812n(k)12253048566776N(r)123767115171238314X:1;(8),,19923:¹3.1N,47454¹3,C(r)=1N26Ni6NjH(r-dij)(3-1)C(r),r(yardstick),dijij,HHeaviside,H(r-dij)=1,dijr0,dijr(3-2)C(r)rC(r)rDS(3-3),(r,C(r)),(3-1),dij(,crowdistance),(,cowdistance)[6]dij,DS1;dij,DS2317Fig.3Theln-lncoordinategraphonthespatialcorrelationdimensionofthecommunicationlinesbasedonthe17citiesinHenan3.2,,,()Q=DS2DS1(3-4)0DS2,DS2DS1,0Q1:Q0.5,;0.5Q1,;Q1,,Q=1,3.3,17()17,,(3,,,,,N2=1717);(3-1)(3-3)DS,N(r)rDS(3-5)N(r)=ijH(r-dij)(3-6)r=575,550,525,,25(,$r=25km),N(r)=289,287,283,,173,(r,N(r)),,4755:,(3-5),DS2=1.344,R2=0.996DS1=1.450,R2=0.997,Q=1.344/1.450=0.927,,17,317(km)XTab.3Amatrixofcowdistancesonthe17maincitiesofHenanProvince0155071226072174970185285210113088105160631760194299144127121190016625718294401571190143181187215328231337309090187117162275178284284700155234157227340243349349956502193741482162852762332832702001980194296158266368282302340153109581350289134360308421239435391315321368508430025727429432944234545142313317718437724240802383172403104233264324041781488325111645116103424213444145274305365082822521873552205552101040X:2;(5),,19944rN(r)Tab.4Yardsticks(r)andthenumbers(N(r))ofthedistanceswhicharemorelongerthantheyardsticks1234567891011121314151617181920212223r575550525500475450425400375350325300275250225200175150125100755025N(r)28928728327927927526525124723721520117716114112997755941311917,,,(),,(3,(fractalline)),,,Steinhaus(paradox):47654,4,,:(1),,,,12(1,2),,02(,0)¹2,(2),,,-,(3),,,,,(),,,()(References)[1]ChenTao.Astudyonthesystemsoftownsasaggregationfractals[J].BulletinofScienceandTechnology,1995,11(2):98101.(InChinese)[.[J].,1995,11(2):98101.][2]LiuJishcng,ChenTao.AfractalstudyonthespatialstructureofsystemsoftownsinNortheastChina[J].ScientiaGeographicaSinica,1995,15(2):136143.(InChinese)[,.[J].,1995,15(2):136143.][3]ThibaultS,MarchardA.ReseauxetTopologie[M].InstitutNationalDesSciencesAppliqueesdeLyon.Villeurbanne,France,1987.[4]BenguiguiL,DaoudM.Isthesuburbanrailwaysystemafractal?[J]GeographicalAnalysis,1991,23:362368.[5]FrankhouserP.Aspectsfractalsdesstructuresurbaines[J].L'EspaceG†ographique,1990,19(1):4569.[6]KayeBH.ARandomWalkThroughFractalDimensions[M].VCHPublishers.NewYork,1989.4775:¹(thinfractals),Hausdorff-BesicovitchAStudyonFractalDimensionsofSpatialStructureofTransportNetworksandtheMethodsofTheirDeterminationLIUJi-sheng1,CHENYan-guang2(1.DepartmentofGeography,NortheastNormalUniversity,Changchun130024;2.DepartmentofGeography,XinyangTeachersCollege,Xinyang,Henan464000)Abstract:Threetypesoffractaldimensionswerepresentedtocharacterizethespatialstructureoftransportnetworks.Thegeographicalmeaningsofthesedimensionswereilluminatedandthemethodsofthedeterminationofthemwereillustrated.Thethreefractaldimensionscanbeexpressedasfollows.1.Length-radiusdimension:itisalwaysdefinedbytheexpressionL(r)rDLwhererisradialdistance,L(r)istotallengthofcommunicationlinesintheareaofPr2,andDListhefractaldimensionreflectingthechangeofdensityofthetransportnetworkaroundameasuredcenter.2.Dendrite-radiusdimension:itcanbegivenbytheformulaN(r)rDbandN(r)isdefinedasN(r)=rk=1n(k)(r=1,2,,k=1,2,,r)whererisgyrationradius,kisordinalnumberofeachringbeltdividedwithr,n(k)istheamountofbranchesofcommunicationlinesinthekthringbelt,andDbisthefractaldimensionrevealingthespatialcomplexingoftransportnetwork.3.Spatialcorrelationdimension:itcanbeexpressed