IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v57y2013icp146-154.html
   My bibliography  Save this article

Dimension of hyperfractals

Author

Listed:
  • Andres, Jan
  • Rypka, Miroslav

Abstract

It is shown that multivalued fractals have the same address structure as the associated hyperfractals. Hyperfractals may be used to model self-similar diffusion limited aggregations, structure of urban settlements, and clusters of nanoparticles. We establish that the Hausdorff dimensions of a particular class of hyperfractals can be calculated by means of the Moran–Hutchinson formula.

Suggested Citation

  • Andres, Jan & Rypka, Miroslav, 2013. "Dimension of hyperfractals," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 146-154.
    • Handle: RePEc:eee:chsofr:v:57:y:2013:i:c:p:146-154
    DOI: 10.1016/j.chaos.2013.10.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077913001938
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2013.10.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chifu, Cristian & Petruşel, Adrian, 2008. "Multivalued fractals and generalized multivalued contractions," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 203-210.
    2. Llorens-Fuster, Enrique & Petruşel, Adrian & Yao, Jen-Chih, 2009. "Iterated function systems and well-posedness," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1561-1568.
    3. Singh, S.L. & Prasad, Bhagwati & Kumar, Ashish, 2009. "Fractals via iterated functions and multifunctions," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1224-1231.
    4. Cinzia Colapinto & Davide Torre, 2008. "Iterated Function Systems, Iterated Multifunction Systems, and Applications," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 83-90, Springer.
    5. Andres, Jan & Fišer, Jiří & Gabor, Grzegorz & Leśniak, Krzysztof, 2005. "Multivalued fractals," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 665-700.
    6. Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "From iterated function systems to iterated multifunction systems," Departmental Working Papers 2008-39, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Prithvi, B.V. & Katiyar, S.K., 2022. "Interpolative operators: Fractal to multivalued fractal," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Ullah, Kifayat & Katiyar, S.K., 2023. "Generalized G-Hausdorff space and applications in fractals," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Llorens-Fuster, Enrique & Petruşel, Adrian & Yao, Jen-Chih, 2009. "Iterated function systems and well-posedness," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1561-1568.
    5. Bucci, Alberto & Florio, Massimo & La Torre, Davide, 2012. "Government spending and growth in second-best economies," Economic Modelling, Elsevier, vol. 29(3), pages 654-663.
    6. Miculescu, Radu & Mihail, Alexandru & Urziceanu, Silviu-Aurelian, 2020. "Contractive affine generalized iterated function systems which are topologically contracting," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. Abbas, Mujahid & Anjum, Rizwan & Iqbal, Hira, 2022. "Generalized enriched cyclic contractions with application to generalized iterated function system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    8. Davide LA TORRE & Edward R. VRSCAY, 2008. "A generalized fractal transform for measure-valued images," Departmental Working Papers 2008-38, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    9. Altun, Ishak & Sahin, Hakan & Aslantas, Mustafa, 2021. "A new approach to fractals via best proximity point," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Vincenzo CAPASSO & Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "Parameter identification for deterministic and stochastic differential equations using the "collage method" for fixed point equations," Departmental Working Papers 2008-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    11. Chifu, Cristian & Petruşel, Adrian, 2008. "Multivalued fractals and generalized multivalued contractions," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 203-210.
    12. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.
    13. Saleem, Naeem & Ahmad, Khaleel & Ishtiaq, Umar & De la Sen, Manuel, 2023. "Multivalued neutrosophic fractals and Hutchinson-Barnsley operator in neutrosophic metric space," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    14. Petruşel, Adrian & Petruşel, Gabriela, 2019. "Coupled fractal dynamics via Meir–Keeler operators," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 206-212.
    15. Jaroszewska, Joanna, 2013. "A note on iterated function systems with discontinuous probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 28-31.
    16. Reny George & Hemanth Kumar Pathak, 2020. "Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    17. Zhang, Yongping & Sun, Weihua & Liu, Shutang, 2009. "Control of generalized Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1738-1744.
    18. Singh, S.L. & Prasad, Bhagwati & Kumar, Ashish, 2009. "Fractals via iterated functions and multifunctions," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1224-1231.
    19. Alberto BUCCI & Herb E. KUNZE & Davide LA TORRE, 2008. "Parameter identification, population and economic growth in an extended Lucas and Uzawa-type two sector model," Departmental Working Papers 2008-34, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:57:y:2013:i:c:p:146-154. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.