Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals

Chaos, Solitons and Fractals

Volumn 41, Issue 2, 2009, Pages 615-629

  Chen, Yanguang ^a   Lin, Jingyi ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

STRUCTURAL OPTIMIZATION;

OPTIMAL STRUCTURES; OPTIMIZATION CONDITIONS; RESPONSE EQUATIONS; SELF-AFFINE FRACTAL MODELS; SELF-AFFINE FRACTALS; SELF-AFFINE STRUCTURES; SELF-SIMILAR FRACTALS; UTILITY MAXIMIZATIONS;

FRACTAL DIMENSION;

EID: 67349154408     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2008.02.035     Document Type: Article

References (34)

1. Arlinghaus S.L. Fractals take a central place. Geogr Ann B 67 2 (1985) 83-88
2. Arlinghaus S.L., and Arlinghaus W.C. The fractal theory of central place geometry: a Diophantine analysis of fractal generators for arbitrary Löschian numbers. Geogr Anal 21 (1989) 103-121
3. Batty M. Fractals: new ways of looking at cities. Nature 377 (1995) 574
4. Batty M., Fotheringham A.S., and Longley P.A. Urban growth and form: scaling, fractal geometry and diffusion-limited aggregation. Environ Plan A 21 (1989) 1447-1472
5. Batty M., and Longley P.A. Fractal cities: a geometry of form and function (1994), Academic Press, London
6. Batty M., and Kim S.K. Form follows function: reformulating urban population density functions. Urban Stud 29 7 (1992) 1043-1070
7. Beckmann M.J. City hierarchies and distribution of city sizes. Econ Develop Cult Change 6 3 (1958) 243-248
8. Benguigui L., Czamanski D., Marinov M., and Portugali J. When and where is a city fractal?. Environ Plan B: Plan Des 27 4 (2000) 507-519
9. von Bertalanffy L. General system theory: foundations, development, and applications (1968), George Braziller, Inc, New York
10. Berry B.J.L. Cities as systems within systems of cities. Pap Reg Sci 13 1 (1964) 146-163
11. Chen Y.G. Fractal urban systems: scaling, symmetry, and spatial complexity (2008), Science Press, Beijing [in Chinese]
12. Chen Y.G., and Zhou Y.X. The rank-size rule and fractal hierarchies of cities: mathematical models and empirical analyses. Environ Plan B: Plan Des 30 6 (2003) 799-818
13. Chen Y.G., and Zhou Y.X. Multi-fractal measures of city-size distributions based on the three-parameter Zipf model. Chaos, Solitons & Fractals 22 4 (2004) 793-805
14. Chen Y.G., and Zhou Y.X. Reinterpreting central place networks using ideas from fractals and self-organized criticality. Environ Plan B: Plan Des 33 3 (2006) 345-364
15. Chen Y.G., and Zhou Y.X. Scaling laws and indications of self-organized criticality in urban systems. Chaos, Solitons & Fractals 35 1 (2008) 85-98
16. De Keersmaecker M.-L., Frankhauser P., and Thomas I. Using fractal dimensions for characterizing intra-urban diversity: the example of Brussels. Geogr Anal 35 4 (2003) 310-328
17. Dendrinos DS, El Naschie MS, editors. Nonlinear dynamics in urban and transportation analysis. Chaos, Soliton & Fractals 1994; 4: 497-617 [special issue].
18. Feng J. Spatial-temporal evolution of urban morphology and land use structure in Hangzhou. Acta Geogr Sin 58 3 (2003) 343-353 [in Chinese]
19. Fotheringham A.S., Batty M., and Longley P.A. Diffusion-limited aggregation and the fractal nature of urban growth. Pap Reg Sci 67 1 (1989) 55-69
20. Frankhauser P. La fractalité des structures urbaines (1994), Economica, Paris
21. Gould S.J. Allometry and size in ontogeny and phylogeny. Biol Rev 41 4 (1966) 587-640
22. Jiang S.G., and Zhou Y.X. The fractal urban form of Beijing and its practical significance. Geogr Res 25 2 (2006) 204-212 [in Chinese]
23. Jullien R., and Botet R. Aggregation and fractal aggregates (1987), World Scientific Publishing Co., Singapore
24. Kaye B.H. A random walk through fractal dimensions (1989), VCH Publishers, New York
25. Knox P.L., and Marston S.A. Human geography: places and regions in global context (1998), Prentice Hall, Upper Saddle River, NJ
26. Lee Y. An allometric analysis of the US urban system: 1960-80. Environ Plan A 21 4 (1989) 463-476
27. Mandelbrot B.B. The fractal geometry of nature (1983), W.H. Freeman and Company, New York
28. Matsuba I., and Namatame M. Scaling behavior in urban development process of Tokyo City and hierarchical dynamical structure. Chaos, Solitons & Fractals 16 1 (2003) 151-165
29. Naroll R.S., and von Bertalanffy L. The principle of allometry in biology and social sciences. Gen Syst Yearbook 1 (1956) 76-89
30. Smeed R.J. Road development in urban area. J Inst Highw Eng 10 (1963) 5-30
31. Tobler W. A computer movie simulating urban growth in the Detroit region. Econ Geogr 46 2 (1970) 234-240
32. Vicsek T. Fractal growth phenomena (1989), World Scientific, Singapore
33. White R., and Engelen G. Cellular automata and fractal urban form: a cellular modeling approach to the evolution of urban land-use patterns. Environ Plan A 25 8 (1993) 1175-1199
34. White R., and Engelen G. Urban systems dynamics and cellular automata: fractal structures between order and chaos. Chaos, Solitons & Fractals 4 4 (1994) 563-583