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Organization Patterns of Complex River Networks in Chile: A Fractal Morphology

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  • Francisco Martinez

    (Escuela de Ingenieria Civil, Pontificia Universidad Catolica de Valparaíso, Av. Brasil 2147, Valparaíso 2340000, Chile)

  • Hermann Manriquez

    (Instituto de Geografia, Pontificia Universidad Catolica de Valparaíso, Av. Brasil 2241, Valparaiso 2340000, Chile)

  • Alberto Ojeda

    (Escuela de Ingenieria Civil, Pontificia Universidad Catolica de Valparaíso, Av. Brasil 2147, Valparaíso 2340000, Chile)

  • Gabriel Olea

    (Escuela de Ingenieria Civil, Pontificia Universidad Catolica de Valparaíso, Av. Brasil 2147, Valparaíso 2340000, Chile)

Abstract

River networks are spatially complex systems difficult to describe by using simple morphological indices. To this concern, fractal theory arises as an interesting tool for quantifying such complexity. In this case of study, we have estimated for the first time the fractal dimension of Chilean networks distributed across the country, analysed at two different scales. These networks insert into variable environments, not only from a climatic and hydrological point of view, but also from a morphological point of view. We investigate to which extent the fractal dimension is able to describe the apparent disorganized character of landscape, by applying two methods. Striking patterns of organization related to Horton ratios and the fractal dimension are reported and discussed. This last parameter depends on the scale of the network, showing interesting groupings by tectonic and climatological factors. Our results suggest that under restricted conditions, the fractal dimension could help to capture the intricate morphology of Chilean networks and its links with the hydrological, climatic, and tectonic conditions present across the country.

Suggested Citation

  • Francisco Martinez & Hermann Manriquez & Alberto Ojeda & Gabriel Olea, 2022. "Organization Patterns of Complex River Networks in Chile: A Fractal Morphology," Mathematics, MDPI, vol. 10(11), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1806-:d:823662
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    References listed on IDEAS

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    1. Pierre Frankhauser, 2008. "Fractal Geometry for Measuring and Modelling Urban Patterns," Springer Books, in: Sergio Albeverio & Denise Andrey & Paolo Giordano & Alberto Vancheri (ed.), The Dynamics of Complex Urban Systems, pages 213-243, Springer.
    2. Alison K. Cheeseman & Edward R. Vrscay, 2022. "Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution," Mathematics, MDPI, vol. 10(5), pages 1-21, March.
    3. Labini, F.Sylos & Gabrielli, A. & Montuori, M. & Pietronero, L., 1996. "Finite size effects on the galaxy number counts: Evidence for fractal behavior up to the deepest scale," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 226(3), pages 195-242.
    4. Isabelle Thomas & Pierre Frankhauser & Dominique Badariotti, 2012. "Comparing the fractality of European urban neighbourhoods: do national contexts matter?," Journal of Geographical Systems, Springer, vol. 14(2), pages 189-208, April.
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    Cited by:

    1. Francisco Martínez & Bastian Sepúlveda & Hermann Manríquez, 2023. "Fractal Organization of Chilean Cities: Observations from a Developing Country," Land, MDPI, vol. 12(2), pages 1-21, January.
    2. Mohammad (Behdad) Jamshidi & Arash Dehghaniyan Serej & Alireza Jamshidi & Omid Moztarzadeh, 2023. "The Meta-Metaverse: Ideation and Future Directions," Future Internet, MDPI, vol. 15(8), pages 1-31, July.

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