An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas

Chaos, Solitons and Fractals

Volumn 39, Issue 1, 2009, Pages 49-64

  Chen, Yanguang ^a   Jiang, Shiguo ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FRACTAL DIMENSION; MATRIX ALGEBRA;

ALLOMETRIC GROWTH; ALLOMETRIC RELATION; ANALYTICAL PROCESS; MATRIX EQUATIONS; SCALING FACTORS; SPATIOTEMPORAL EVOLUTION; URBAN DEVELOPMENT; URBAN SYSTEMS;

URBAN GROWTH;

EID: 60649087566     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.01.130     Document Type: Article

References (40)

1. Arlinghaus S. Fractals take a central place. Geografiska Annaler B 67 2 (1985) 83-88
2. Batty M. Cities as fractals: simulating growth and form. In: Crilly A.J., Earnshaw R.A., and Jones H. (Eds). Fractals and chaos (1991), Springer-Verlag, New York 43-69
3. Batty M., and Longley P. Urban shapes as fractals. Area 19 (1987) 215-221
4. Batty M., and Longley P.A. Fractal cities: a geometry of form and function (1994), Academic Press, London
5. Benguigui L., Czamanski D., Marinov M., and Portugali J. When and where is a city fractal?. Environment and Planning: Planning and Design 27 (2000) 507-519
6. Berry B.L.J. Cities as systems within systems of cities. Papers of the Regional Science Association 13 (1964) 147-163
7. von Bertalanffy L. General system theory: foundations, development and applications (1968), George Braziller, Inc., New York
8. Boyce R. Changing patterns of urban land consumption. Professional Geographer 15 (1963) 19-24
9. Chen Y.G. The allometric models on the relationships between area and population of urban systems: underlying rationale, generalized equation, and empirical analyses. Journal of Central China Normal University (Nat. Sci.) 36 2 (2002) 375-380 [in Chinese]
10. Chen Y.G., and Wang Y.J. A fractal study on interaction between towns in urban systems. Bulletin of Science and Technology 13 4 (1997) 233-237 [in Chinese]
11. Chen Y.G., and Luo J. A dynamic similarity analysis of fractal structure of the City of Zhengzhou: 1985-1998. Economic Geography 21 4 (2001) 389-393 [in Chinese]
12. Chen Y.G., and Zhou Y.X. Researches in models of allometric analysis of urban systems and forecast of urbanization level based on RS data of urban area. Acta Scientiarum Naturalium Universiitatis Pekingensis 37 6 (2001) 819-826 [in Chinese]
13. Chen Y.G., and Zhou Y.X. The rank-size rule and fractal hierarchies of cities: mathematical models and empirical analyses. Environment and Planning B: Planning and Design 30 (2003) 799-818
14. Chen Y.G., and Zhou Y.X. Multifractal measures of city-size distributions based on the three-parameter Zipf model. Chaos, Soliton & Fractals 22 (2004) 793-805
15. Dutton G. Foreword: size and shape in the growth of human communities. Ekistics 36 (1973) 142-243
16. Feng J. On the industrial decentralization of Hangzhou City. Urban Planning Forum 2 (2002) 42-47 [in Chinese]
17. Frankhauser P. La Fractalité des Structures Urbaines (1994), Economica, Paris
18. Gabaix X., and Ioannides Y. The evolution of city size distributions. In: Henderson J.V., and Thisse J.F. (Eds). Handbook of urban and regional economics. Cities and geography vol. 4 (2004), North-Holland 2341-2378 [Chapter 53]
19. Gould S.J. Allometry and size in ontogeny and phylogeny. Biological Reviews 41 (1966) 587-640
20. He J.-H. An allometric scaling law between gray matter and white matter of cerebral cortex. Chaos, Solitons & Fractals 27 4 (2006) 864-867
21. He J.-H., and Huang Z. A novel model for allometric scaling laws for different organs. Chaos, Solitons & Fractals 27 4 (2006) 1108-1114
22. Knox P.L., and Marston S.A. Places and regions in global context: human geography (1998), Prentice Hall, Upper Saddle River, NJ
23. Lee Y. A stochastic model of the geometric patterns of urban settlements and urban spheres of influence: a clumping model. Geographical Analysis 4 (1972) 51-64
24. Lee Y. An allometric analysis of the US urban system: 1960-80. Environment and Planning A 21 (1989) 463-476
25. Liu J.S., and Chen Y.G. An allometric analysis of the Changchun system of towns: 1949-1988. Human Geography 15 3 (2000) 6-12 [in Chinese]
26. Mandelbrot B.B. Fractals: form chance and dimension (1977), W.H. Freeman and Company, San Francisco
27. Mandelbrot B.B. The fractal geometry of nature (1983), W.H. Freeman and Company, New York
28. Nicolis G., Nicolis C., and Nicolis J. Chaotic dynamics, Markov partitions, and Zipf's law. Journal of Statistical Physics 54 (1989) 915-924
29. Nordbeck S. Urban allometric growth. Geografiska Annaler B 53 (1971) 54-67
30. Rigon R., Rodriguez-Iturbe I., and Rinaldo A. Feasible optimality implies Hack's law. Water Resources Research 34 11 (1998) 3181-3189
31. Satty T.L. The analytical hierarchy process: planning, priority setting, resource allocation (1980), McGraw-Hall, New York
32. Saaty T.L. Decision making for leaders: the analytical hierarchy process for decisions in a complex world (1982), Lifetime Learning Publications, Belmont, Calif
33. Sanders L., Pumain D., Mathian H., Guérin-Pace F., and Bura S. SIMPOP: a multiagent system for the study of urbanism. Environment and Planning B: Planning and Design 24 2 (1997) 287-305
34. Stewart J.Q., and Warntz W. Physics of population distribution. Journal of Regional Science 1 (1958) 99-123
35. Wang F.H. Regional density functions and growth patterns in major plains of China: 1982-1990. Papers in Regional Science 80 (2001) 231-240
36. West B.J., and Griffin L. Allometric control, inverse power laws and human gait. Chaos, Solitons, & Fractals 10 9 (1999) 1519-1527
37. White R., and Engelen G. Urban systems dynamics and cellular automata: fractal structures between order and chaos. Chaos, Solitons & Fractals 4 (1994) 563-583
38. Wilson A.G. Complex spatial systems: the modelling foundations of urban and regional analysis (2000), Pearson Education Asia Pte Ltd, Singapore
39. Woldenberg M.J. An allometric analysis of urban land use in the United States. Ekistics 36 (1973) 282-290
40. Wong D., and Fotheringham A.S. Urban systems as examples of bounded chaos: exploring the relationship between fractal dimension, rank-size, and rural to urban migration. Geografiska Annaler B 72 (1990) 89-99