Reinterpreting central place networks using ideas from fractals and self-organized criticality

Environment and Planning B: Planning and Design

Volumn 33, Issue 3, 2006, Pages 345-364

  Chen, Yanguang ^a   Zhou, Yixing ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CENTRAL PLACE THEORY; CRITICAL ANALYSIS; FRACTAL ANALYSIS; SELF ORGANIZATION;

CENTRAL EUROPE; EURASIA; EUROPE; GERMANY;

EID: 33745124368     PISSN: 02658135     EISSN: None     Source Type: Journal    
DOI: 10.1068/b31131     Document Type: Article

References (55)

1. Allen P M, 1997 Cities and Regions as Self-organizing Systems: Models of Complexity (Gordon and Breach, Amsterdam)
2. Allen P M, Sanglier M, 1979, "A dynamic model of growth in a central place system" Geographical Analysis 11 156-272
3. Allen P M, Sanglier M, 1981, "Urban evolution: self-organization, and decisionmaking" Environment and Planning A 13 167-183
4. Andersson C, Rasmussen S, White R, 2002, "Urban settlement transitions" Environment and Planning B: Planning and Design 29 841-865
5. Arlinghaus S L, 1985, "Fractals take a central place" Geografiska Annaler B 67 83-88
6. Arlinghaus S L, 1990, "Beyond the fractal" Solstice: An Electronic Journal of Geography and Mathematics 1(1), http://www. imagenet.org/
7. Arlinghaus S L, Arlinghaus W C, 1989, "The fractal theory of central place geometry: a Diophantine analysis of fractal generators for arbitrary Loschian numbers" Geographical Analysis 21 103-121
8. Arlinghaus S L, Arlinghaus W C, 2004, "Geometric visualization of hexagonal hierarchies: animation and virtual reality" Solstice: An Electronic Journal of Geography and Mathematics 15(1), http://www.imagenet.org/
9. Bak P, 1996 How Nature Works: The Science of Self-organized Criticality (Springer, New York)
10. Banavar J R, Colaiori F, Flammini A, Maritan A, Rinaldo A, 2001, "Scaling, optimality, and landscape evolution" Journal of Statistical Physics 104(1-2) 1-48
11. Barabási A-L, Bonabeau E, 2003, "Scale-free networks" Scientific American 288(5) 50-59
12. Barbera L, Rosso R, 1989, "On the fractal dimension of stream networks" Water Resources Research 25 735-741
13. Batty M, 1991, "Generating urban forms from diffusive growth" Environment and Planning A 23 511-544
14. Batty M, 2000, "Less is more, more is different: complexity, morphology, cities, and emergence" Environment and Planning B: Planning and Design 27 167-168
15. Batty M, Longley P, 1994 Fractal Cities: A Geometry of Form and Function (Academic Press, London)
16. Batty M, Xie Y, 1999, "Self-organized criticality and urban development" Discrete Dynamics of Nature and Society 3(2-3) 109-124
17. Batty M, Couclelis H, Eichen M, 1997, "Urban systems as cellular automata" Environment and Planning B: Planning and Design 24 159-164
18. Beckmann M J, 1958, "City and hierarchies and distribution of city size" Economic Development and Cultural Change 6 243-248
19. Benguigui L, Czamanski D, Marinov M, Portugali Y, 2000, "When and where is a city fractal?" Environment and Planning B: Planning and Design 27 507-519
20. Bossomaier T, Green D, 1998 Patterns in the Sand: Computers, Complexity and Life (Allen and Unwin, Sydney)
21. Bura S, Guérin-Pace F, Mathian H, Pumain D, Sanders L, 1996, "Multiagent systems and the dynamics of a settlement system" Geographical Analysis 28 161-178
22. Chen Y G, 1998, "An empirical analysis of Koch snowflake model of urban system: fractals and fractal dimension of central place system (with k=3)" Economic Geography 18(4) 33-37 (in Chinese)
23. Chen Y G, Li H Q, 1994, "A Koch snowflake model of urban systems: a possible complement to Christaller's central place theory" Economic Geography 14(3) 10-14 (in Chinese)
24. Chen Y G, Liu J S, 2002, "Derivations of fractal models of city hierarchies using entropy-maximization principle" Progress in Natural Science 12 208-211
25. Chen Y G, Zhou Y X, 2003, "The rank-size rule and fractal hierarchies of cities: mathematical models and empirical analyses" Environment and Planning B: Planning and Design 30 799-818
26. Christaller W, 1933 Central Places in Southern Germany translated in 1966 by C W Baskin (Prentice-Hall, Englewood Cliffs, NJ)
27. Christaller W, 1968 De Guo Nan Bu Zhong Xin Di Yuan Li translated in 1998 by Z Chang, X Wang from Christaller Die Zentralen Orte in Süddeutschland [Central places in southern Germany] (Commercial Press, Beijing)
28. Dacey M F, 1965, "The geometry of central place theory" Geografiska Annaler 47B 111-124
29. Evans A W, 1985 Urban Economics: An Introduction (Basil Blackwell, New York)
30. Goldenfeld N, Kadanoff L P, 1999, "Simple lessons from complexity" Science 284(2) 87-89
31. Hack J T, 1957, "Studies of longitudinal streams profiles in Virginia and Maryland" U.S. Geological Survey Professional Papers B 294 45-97
32. Horton R E, 1945, "Erosional development of streams and their drainage basins: hydrophysical approach to quantitative morphology" Bulletin of the Geophysical Society of America 56 275-370
33. Kauffman S, 1993 The Origin of Order (Oxford University Press, New York)
34. Kaye B H, 1989 A Random Walk Through Fractal Dimensions (VCH, New York)
35. King L J, Golledge R G, 1978 Cities, Space, and Behavior: The Elements of Urban Geography (Prentice-Hall, Englewood Cliffs, NJ)
36. Lee Y, 1989, "An allometric analysis of the US urban system: 1960-80" Environment and Planning A 21 463-476
37. Lösch A, 1940 The Economics of Location translated in 1954 by W H Woglom, W R Stolper (Yale University Press, New Haven, CT)
38. Mandelbrot B B, 1983 The Fractal Geometry of Nature (W H Freeman, New York)
39. Portugali J, 2000 Self-organization and the City (Springer, Berlin)
40. Prigogine I, Stengers I, 1984 Order out of Chaos: Man's New Dialogue with Nature (Bantam Books, New York)
41. Richards A, 2002, "Complexity in physical geography" Geography 87(2) 99-107
42. Rodriguez-Iturbe I, Rinaldo A, 2001 Fractal River Basins: Chance and Self-organization paperback edition (Cambridge University Press, New York)
43. Ryabko B Ya, 1986, "Noise-free coding of combinatorial sources, Hausdorff dimension and Kolmogorov complexity" Problemy Peredachi Informatsii 22 16-26
44. Sanders L, Pumain D, Mathian H, Guérin-Pace F, Bura S, 1997, "SIMPOP: a multiagent system for the study of urbanism" Environment and Planning B: Planning and Design 24 287-305
45. Schumm S A, 1956, "Evolution of drainage systems and slopes in badlands at Perth Amboy, New Jersey" Geological Society of America Bulletin 67 597-646
46. Strahler A E, 1952, "Hypsometric (area-altitude) analysis of erosional topography" Geological Society of America Bulletin 63 1117-1142
47. Taylor J C, 2001 Hidden Unity in Nature's Laws (Cambridge University Press, Cambridge)
48. Turcotte D L, 1997 Fractals and Chaos in Geology and Geophysics 2nd edition (Cambridge University Press, Cambridge)
49. Vicsek T, 1989 Fractal Growth Phenomena (World Scientific Publishing, Singapore)
50. Weyl H, 1980 Symmetry (Princeton University Press, Princeton, NJ)
51. White R, Engelen G, Uljee I, 1997, "The use of constrained cellular automata for high-resolution modelling of urban land-use dynamics" Environment and Planning B: Planning and Design 24 323-343
52. Woldenberg M J, 1979, "A periodic table of spatial hierarchies", in Philosophy in Geography Eds S Gale, G Olsson (D Reidel, Dordrecht) pp 429-456
53. Woldenberg M J, Berry B J L, 1967, "Rivers and central places: analogous systems?" Journal of Regional Science 7 129-139
54. Zhong Y X, 1988 Principle of Information Science (Fujian People's Publishing House, Fuzhou) (in Chinese)
55. Zipf G K, 1949 Human Behavior and the Principles of Least Effort (Addison-Wesley, Reading, MA)