Fractal Analysis of Transport Networks

TitleFractal Analysis of Transport Networks
Publication TypeJournal Article
Year of Publication2011
AuthorsShevchuk, Ya.V
Short TitleNauka innov.
DOI10.15407/scin7.03.005
Volume7
Issue3
SectionScientific Basis of Innovation Activity
Pagination5-13
LanguageUkrainian
Abstract
The new method of fractal analysis of transport networks (in particular city), which provides an estimation of their self-organization degree, is considered. It is established that real fractal dimension of transport networks, which is selforganized by transport vehicles, equals 1,22 and is typical for disordered polymeric fibers and channels formed by fluid flow through porous materials.
Keywordscomplex transport network, fractal analysis, fractal dimension
References
1. Batty M., Longley P., Fotheringham A. Urban growth and form: scaling, fractal geometry, and diffusion-limited aggregation. Environment and Planning. 1989. A 21. P. 1447-1472.
2. Chen Y., Luo, J. The fractal features of the transport network of Henan Province. J. of Xinyang Teachers College. 1998. 11(2): 172-177.
3. Rodin V., Rodina E. The fractal dimension of Tokyo's streets. Fractals. 2000. V. 8. P. 413-418.
https://doi.org/10.1142/S0218348X00000457
4. Shen G. A fractal dimension analysis of urban transportation networks. Geographical and Environmental Modelling. 1997. V. 1. P. 221-236.
5. Benguigui L., Daoud M. Is the Suburban Railway System a Fractal? Geographical Analysis. 1991. V. 23. P. 363-368.
https://doi.org/10.1111/j.1538-4632.1991.tb00245.x
6. Song C., Havlin S., Makse H.A. Self-similarity of complex networks. Nature (London). 2005. V. 433. P. 392-395.
https://doi.org/10.1038/nature03248
7. Song C., Havlin S., Makse H.A. Origins of fractality in the growth of complex networks. Nature Physics. 2006. V. 2. P. 275-281.
https://doi.org/10.1038/nphys266
8. Shahturin D.V. Modelirovanie informacionnyh dannyh v bol'shih setjah. Elektronika i informacion nye tehnologii (Elektronnyj zhurnal). 2009. No 2(7) [in Russian].
9. Benguigui L., Daoud M. Is the Suburban Railway System a Fractal? Geographical Analysis. 1991. 23(4): 362-368.
https://doi.org/10.1111/j.1538-4632.1991.tb00245.x
10. Batty M. Cities as Fractals: Simulating Growth and Form. Fractal and Chaos. Ed. By A.Grilly, R Earnashaw, H. Jones. N.Y.: Springer, 1991. P. 43-69.
11. Mandelbrot B. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science. 1967. 156. P. 636-638.
https://doi.org/10.1126/science.156.3775.636
12. Cit. po: Dubovikov M.M., Krjanev A.V., Starchenko N.V. Razmernost' minimal'nogo pokrytija i lokal'nyj analiz fraktal'nyh vremennyh rjadov. Vestnik RUDN. T3. 2004. No 1: 81-95 [in Russian].
13. Aleksandrov P.S., Pasynkov B.A. Vvedenie v teoriju razmernosti. Moskva: Nauka, 1973 [in Russian].
14. Hausdorff F. Dimesion und Ausseres Mass. Matematishe Annalen. 1919. V. 79. P. 157-179.
15. Kronover R.M. Fraktaly i haos v dinamicheskih siste mah. Osnovy teorii. Moskva: Postmarket, 2000 [in Russian].
16. Feder E. Fraktaly: Per. s angl. Moskva: Mir, 1991.
17. Kravchenko O.V., Masjuk V.M. Komp'juternoe modelirovanie fizicheskih processov na osnove fraktal'nyh funkcij. Elektronnoe nauchno-tehnicheskoe izdanie «Nauka i obrazovanie». 2005. No 2. http://technomag.edu.ru/doc/49299.html [in Russian]
18. Morency C., Chapleau R. Fractal geometry for the characterisation of urban-related states: Greater Montreal Case. HarFA — Harmonic and Fractal Image Analysis (e-journal). 2003. P. 30-34.
http://www.fch.vutbr.cz/lectures/imagesci (www.fch.vutbr.cz/lectures/imagesci/download_ejournal/09...).
19. HARFA, Harmonic and Fractal Image Analyser, Software for the Determination of Fractal Dimension, www.fch.vutbr.cz/lectures/imagesci
20. Bourke P. Fractal Dimension Calculator. local.wasp.uwa.edu.au/ pbourke/fractals/fracdi.
21. Roy A., Perfect E., Dunne W. M., McKay L. D. (2007), Fractal characterization of fracture networks: An improved box-counting technique, J. Geophys. Res., 112, B12201.
https://doi.org/10.1029/2006JB004582
22. Lu Y, Tang J. Fractal dimension of a transportation network and its relationship with urban growth: a study of the Dal las — Fort Worth area. Environment and Planning B: Planning and Design. 2004. 31(6): 895-911.
https://doi.org/10.1068/b3163
23. Tang J. Evaluating the relationship between urban road pattern and population using fractal geometry.
www.ucgis.org/summer03/studentpapers/junmeitang.pdf
24. Sun Z., Jia P., Kato H., Hayashi Y. Distributive Continuous Fractal Analysis for Urban Transportation Network. Proceedings of the Eastern Asia Society for Transportation Studies. 2007. Vol. 6. P. 1519-1531. www.unagoya-u.ac.jp/sustain/paper/2007/kokusai/...
25. Apostolos L. Simulating Urban Growth through Cellular Automata: A New Way of Exploring the Fractal Nature of Urban Systems. http://users.auth.gr/alagaria/SIMULATION.pdf
26. Malineckij G.G. Novaja real'nost' i budushhee glazami sinergetiki. http://www.smi-svoi.ru/content/?fl= 590&sn=1469 [in Russian].
27. Evdokimov Ju.K., Shahturin D.V. Issledovanie informacionnyh potokov dannyh v telekommunikacionnyh setjah. fetmag.mrsu.ru/.../pdf/Information_data_flow.pdf [in Russian].
28. Stryhaljuk B.M. Fraktal'nyj sposib prognozuvannja potokiv u mul'tyservisnyh merezhah. Radioelektronika ta telekomunikacii'. Visnyk NU «L'vivs'ka politehnika». 2009. No 645. S. 88-95 [in Ukrainian].
29. Starchenko V.N. Ekonofizika i analiz finansovyh vremennyh rjadov. http://am.intrast.ru/analytics.php?id_analitika=13... [in Russian]
30. Evdokimov Ju.K., Shahturin D.V. Analiz sistemnyh svojstv bol'shih kommunikacionnyh setej na primere topologii rossijskih zheleznodorozhnyh dorog. Zhurnal «Nelinejnyj mir». 2010. No 5. C. 297-301 [in Russian].
31. Cieplak M., Maritan A., Banavar J. Optimal paths and domain walls in the strong disorder limit. Phys. Rev. Lett. 1994. V. 72. P. 2320-2324.
https://doi.org/10.1103/PhysRevLett.72.2320
32. Cieplak M., Maritan A., Banavar J. Optimal paths and domain walls in the strong disorder limit. Phys. Rev. Lett. 1994. V. 72. P. 2320-2324.
https://doi.org/10.1103/PhysRevLett.72.2320
33. Cieplak M., Maritan A., Banavar J. Invasion percolation and Eden growth: Geometry and universality. Phys. Rev. Lett. 1996. V. 76. P. 3754-3757.
https://doi.org/10.1103/PhysRevLett.76.3754
34. Dobrin R., Duxbury P.M. Minimum Spanning Trees on Ran dom Networks. Phys. Rev. Lett. 2001. V. 86. P. 5076.
https://doi.org/10.1103/PhysRevLett.86.5076
35. Andrade J.S., Saulo Jr., Reis D.S., et all. Ubiquitous fractal dimension of optimal paths. Computing in Science and Engineering. 2011. V. 13, No. 1. P. 74-81. www.comphys.ethz.ch/hans/p/528.pdf
https://doi.org/10.1109/MCSE.2011.16
36. Braess's paradox. en.wikipedia.org/wiki/Braess%27_paradox