ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ivanov A. V., Koronovskii A. A., Minjuhin I. M., Yashkov I. A. Definition of the fractal dimension of Saratov ravine network. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 2, pp. 64-74. DOI: 10.18500/0869-6632-2006-14-2-64-74

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 190)
Article type: 

Definition of the fractal dimension of Saratov ravine network

Ivanov Aleksej Viktorovich, Yuri Gagarin State Technical University of Saratov
Koronovskii Aleksei Aleksandrovich, Saratov State University
Minjuhin Igor Mihajlovich, Saratov State University
Yashkov Ivan Aleksandrovich, Saratov State University

Fractal analysis of natural self-similar structures has been considered. Different approaches to the analysis of abstract mathematical fractals and natural fractals have been described. Numerical method of the fractal dimension calculation has been suggested. This method has been applied both for the model fractal (Sierpinski carpet) and natural fractals ´ (Saratov ravine network). 

Key words: 
  1. Koronovsky AA, Trubetskov DI. Nonlinear dynamics in action: How the ideas of nonlinear dynamics penetrate ecology, economics and social sciences. Saratov: Kolledg; 2002. 330 p.(In Russian).
  2. Yashkov IA, Ivanov AV. The study of the erosion network using fractal analysis. Nedra Povolgya i Prikaspiya. 2005;44:49–58. (In Russian).
  3. Vasiliev LN. Fractality and self-similarity of natural spatial structures. Izvestiya RAN. Seriya Geograficheskaya. 1992;5:25–35.
  4. Puzachenko YuG. Application of fractal theory to the study of landscape structure. Izvestiya RAN. Seriya Geograficheskaya. 1997;2:24–40.
  5. Claps P, Oliveto G. Reexamining the determination of the fractal dimension of river networks. Water Resour. Res. 1996;32(10):3123–3136. DOI: 10.1029/96WR01942.
  6. Barbera LP, Rosso R. On the fractal dimension of stream networks. Water Resour. Res. 1989;25(4):735–741. DOI: 10.1029/WR025I004P00735.
  7. McNamara JP, Kane DL, Larry D, Hinzman LD. An analysis of an arctic channel network using a digital elevation model. Geomorphology. 1999;29:339–353.
  8. Lopes C. de O, Paula GA. de, Vieira AC. Fractalidade da estrutura de drenagen do municipio do Rio de Janeiro. Revista Universidade Rural, Serie Clenclas Exalas e da Terra. 2002;21(2):23.
  9. Mandelbrot B. The fractal geometry of nature. San Francisco: W.H. Freeman; 1982. 443 p.(In Russian).
  10. Feder J. Fractals. New York: Plenum Press; 1991. 254 p.
  11. Kuznetsov SP. Dynamic chaos. Moscow: Fizmatlit; 2001. 296 p. (In Russian).
  12. Artemyev SA. et al. Saratov: comprehensive geoecological analysis. Ed. AV. Ivanova. Saratov: Saratov University Publishing; 2003. (In Russian).
  13. Manzhurov IL. Fractal model of distribution of density of surface contaminants. Abstract of the dissertation for the degree of candidate of physical and mathematical sciences. Yekaterinburg. 2002. 24 p. (In Russian).
  14. Koronovsky AA, Rempen IS, Trubetskoy DI, Temov AE. Transitional chaos in a distributed active environment "screw electron beam - oncoming electromagnetic wave". Bulletin of the Russian Academy of Sciences: Physics. 2002;66(12):1754–1760.
  15. Khudyakov GI, Nikiforov AN. On the geomorphological structure of the territory of the city of Saratov. Problems of geomorphology and morphotectonics. Saratov: Kolledg; 1998. P. 46. (In Russian).
Short text (in English):
(downloads: 126)