GEO GRA P HICAL RESEA RCH

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1 GEO GRA P HICAL RESEA RCH Vol125, No12 Mar1, ,2, 1 (11, ; 21, ) : Landsat TM,,,, ,, : ; ; ; ; ; : (2006) , 1985 Batty [1 ], : Batty Longley [ 2,3 ], Frankhauser [4,5 ], Batty Longley Fot heringham White Engelen [6 9 ], Benguigui Tel Aviv, [10 ] 1992 [11 ], [12 ], [ 13,14 ], [15,16 ] ; - ( ) [ ] ;, [20 ] ; , [21 ],,,, : ; : : ( ) : (19782),,,, E2mail :

2 2 : 205 (box2counting met hod),,,, (area2radius relationship met hod),, [8 ], Batty Longley (1987/ 1988) Benguigui (2000) (2000) (2000) (2003), White Engelen (1993), [ 8 ] ;, (2004) [ 21 ],,, ( ), 2, [10,20 ], r, M ( r) ; r, M ( r) M ( r) M ( r) :, M ( r) r,,,, = D, D :, ;,, ;, 1, ; ( S) ( N),, S ( N) N,,, ( scaling range),,,, R 2 c Benguigui R c 0104 [10 ],, 3 311,,,,

3 Landsat 5 TM, , , 20 ( GCP),,,, 30m,, R M S error 15m,,,,,,,,, (CBD) CBD [22 ], CBD [23 ], CBD, 6 ( ),, [ 24 ] [25 ],,,,, 015km 1km 115km, 30km ( ),,,, 015km, 70 ( 1 1) Arc GIS Microsoft Access Microsoft Excel, ,, ( ) 312 2, ( 2) 2,,,,, D R 2 N ( ),, ( ), Batty ( Fractal Signat ure) [7 ] D R 2 N, : , , 2 2, , 1984,, ,,, 1984, 16,, = 8km, 1984, 8km , = 14km, 1984

4 2 : Fig12 The plots on fractal dimensions of Beijing in log2log coordinate 411,, [16 ] L S V : L 1/ 1 S 1/ 2 V 1/ 3 M 1/ d, M ( L S V ), d (, d = 1, 2 3),, d, r L, L r, 2,, D, r 1/ 1 S ( r) 1/ D, S ( r) = k r D (1) k, D r A ( r),, (1), A ( r) = r 2 (2) da ( r) d r ds ( r) d r = 2 r (3) = D k r D - 1 (4)

5 (3) (4), ( r) = ds ( r) da ( r) rd - 2 (5) Smeed [ 7 ], ( r) r : D < 2, ( r) 1/ r 2 - D, r, ( r), ; D = 2, ( r) = D k,, ; 2 D > 2, ( r) r D - 2, r, ( r),, D > 2,, D > 2, White ( 1) 1 Tab11 The dimensions of four American cities on different land use types : White R and Engelen (1993), [ 8 ], : (1) ; (2) ; (3) ;,,,, (CBD), 2, 2 Tab12 The change of fractal dimensions of Beijing ( built2up area) R 2 R km km > 10km > 1615km 2,, ,, ( ) 1984,, D 21007, 2109, 2, 19 ( D = 2 ), D 2, 1984, 3, ,

6 2 : 209,,,,,,, 5, 33 :,, ;,, 412, 41211,,,,, 3,,, [26 ],, 8 [26 ],,,,, [26 ],,,,, [26 ],,, :,,,,,,, [ 27 ],,, 41212,, r S ( r) S ( r) = k r D, ,,,,,, 3,, :

7 ( 1984,1999) Tab1 3 The comparison of the scaling range of built2up area in Beijing in 1984 and D = 2 D = (km) (km 2 ) (km 2 ) ( %) :,, ( ),30m TM,,,,,,,,, , D = 2, , : (1),,, (2),,,, (3),, 5,, km ( ) km,,1984, 10km,, 1999, 1615km,,,,

8 2 : 211 :, : [ 1 ] Batty M1 Fractals2geometry between dimensions1 New Scientist, 1985, 106 : [ 2 ] Batty M, Longley P A1 Urban shapes as fractals1 Area, 1987, 19 : [ 3 ] Batty M, Longley P A1 The morphology of urban land use1 Environment and Planning B : Planning and Design, 1988, 15 : [ 4 ] Frankhauser P1 Aspect s fractals des structures urbaines1 L Espace Geographique, 1990, 19 : [ 5 ] Frankhauser P1 La Fractalit des Structures Urbaines1 Paris : Economica, [ 6 ] Batty M, Longley P A, Fot heringham A S1 Urban growt h and form : scaling, fractal geometry and diffusion2limit2 ed aggregation1 Environment and Planning A, 1989, 21 : [ 7 ] Batty M, Longley P A1 Fractal Cities : A Geometry of Form and Function1 London : Academic Press, Harcourt Brace & Company Publishers, [ 8 ] White R, Engelen G1 Cellular automata and fractal urban form : a cellular modeling approach to t he evolution of urban land2use patterns1 Environment and Planning A, 1993, 25 : [ 9 ] White R, Engelen G, Uljee I1 The use of constrained cellular automata for high2resolution modeling of urban2land dynamics1 Environment and Planning B : Planning and Design, 1997, 24 : [ 10 ] Benguigui L, Czamanski D, Marinov M, et al1 When and where is a city fractal? Environment and Planning : Plan2 ning and Design, 2000, 27 : [ 11 ], 1.,1992,12 (4) :1 51 [ 12 ], 1.,2000,20 (2) : [ 13 ], 1 :.,2001,20 (2) : [ 14 ], 1 1 ( ),2001,14 (2) : ,2191 [ 15 ], 1 DL A DBM 1 ( ),2001,14 (3) : [ 16 ], 1 : 1 ( ),2002,15 (1) : [ 17 ], 1 1,2000,23 (4) : [ 18 ] 1 1,2000,55 (6) : [ 19 ] 1 1,2004,24 (1) : [ 20 ] 1 1,2003,58 (3) : [ 21 ],, 1 1,2004,23 (2) : [ 22 ] Yan X1 Chinese urban geography since t he late 1970s1 Urban Geography, 1995, 16 : [ 23 ] 1 1,2002, (2) : [ 24 ] Wang F H, Zhou Y X1 Modeling urban population densities in Beijing : suburbanisation and it s causes1 Urban Studies, 1999, 36 : [ 25 ], ,2003,58 (6) : [ 26 ] 1 1 :,19951 [ 27 ] Zhou Y X1 Definitions of urban places and statistical standards of urban population in China : problems and solu2 tions1 Asian Geographer, 1988, 7 :

9 The fractal urban f orm of Beijing and its practical signif icance J IAN G Shi2guo 1,2, ZHOU Yi2xing 1 (11 Geographic Science Research Center, Peking University, Beijing , China ; 21 Urban Planning & Design Institute, Tsinghua Universty,Beijing ,China) Abstract :This paper present s a study on t he f ractal urban form of Beijing1 We use t he city built2up area to define t he urban form1 It includes all the built2up area of houses, squares and roads, but the roads connecting central cities are not included, nor t he water and vege2 tation1 The data is obtained f rom the Landsat TM images of Beijing1 Two TM scenes from 1984 and 1999 are used to cover t he city and it s adjacent areas1based on t he unsupervised classification using t he IMA GIN E ERDAS 816, t he authors conducted an aborative correc2 tion on t he map so t hat t he classification is accurate enough1 ESRI ARC GIS 91 0 is used to get the area data1 The authors use t he area2radius relationship met hod in this paper1 In t his view, the fractal dimension is a way to clarify t he convergence and decentralization of urbanized area1 The authors found t hat t he city of Beijing bears clear f ractal characteristics1 The com2 p utation shows t hat t here exist double scaling range1 The first scaling range is good to re2 veal t he f ractal evolution of Beijing1 The scaling range is 8km in 1984 while it is 14km in The extensio n of t he scaling range shows t hat t he f ractal characteristic in 1999 is better than t hat in The dimension values also indicate the building density of Bei2 jing1 In 1984, t he density remains almost unchanged in a region of 10 km distance f rom t he center ( Tian an Men)1 In 1999, t he building density increases f rom t he center to a region with a radius of 1615 km1 Both of t he building densities decrease out side t he corresponding ranges of 1984 and The f ractal model f rom t he area2radius relationship met hod in t his paper has important t heoretical significance, which needs f urt her st udies1 The f ractal comp utation in t his paper has important practical significance1 The scaling range of a city is a special variable t hat carries individual characteristics1 It is also a compa2 rable variable among cities1 Based on this, t he aut hors identified a new city definition u2 sing t he scaling range1 The new definition can avoid the subjective and incomparable fac2 tor s of t he ordinary definitio n met hod1 The scaling range also has important t heoretical significance1 Key words :urban form ; remote sensing image ; f ractal ; f ractal dimensio n ; area2radius rela2 tionship met hod ; Beijing

GEO GRAPHICAL RESEARCH

22 4 2003 7 GEO GRAPHICAL RESEARCH Vol. 22, No. 4 J uly, 2003-1, 2, 3 (11, 130024 ; 21, 100871 ; 31, 210096) : - -, ; -, - (U GC) -, : ; ; ; ; : F06115 ; KP2815 : 100020585 (2003) 0420447208 1 - [1 ],,