IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v39y2009i3p1224-1231.html
   My bibliography  Save this article

Fractals via iterated functions and multifunctions

Author

Listed:
  • Singh, S.L.
  • Prasad, Bhagwati
  • Kumar, Ashish

Abstract

Fractals have wide applications in biology, computer graphics, quantum physics and several other areas of applied sciences (see, for instance [Daya Sagar BS, Rangarajan Govindan, Veneziano Daniele. Preface – fractals in geophysics. Chaos, Solitons & Fractals 2004;19:237–39; El Naschie MS. Young double-split experiment Heisenberg uncertainty principles and cantorian space-time. Chaos, Solitons & Fractals 1994;4(3):403–09; El Naschie MS. Quantum measurement, information, diffusion and cantorian geodesics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 191–205; El Naschie MS. Iterated function systems, information and the two-slit experiment of quantum mechanics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 185–9; El Naschie MS, Rossler OE, Prigogine I. Forward. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995; El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals 2004;19:209–36; El Naschie MS. Fractal black holes and information. Chaos, Solitons & Fractals 2006;29:23–35; El Naschie MS. Superstring theory: what it cannot do but E-infinity could. Chaos, Solitons & Fractals 2006;29:65–8). Especially, the study of iterated functions has been found very useful in the theory of black holes, two-slit experiment in quantum mechanics (cf. El Naschie, as mentioned above). The intent of this paper is to give a brief account of recent developments of fractals arising from IFS. We also discuss iterated multifunctions.

Suggested Citation

  • Singh, S.L. & Prasad, Bhagwati & Kumar, Ashish, 2009. "Fractals via iterated functions and multifunctions," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1224-1231.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1224-1231
    DOI: 10.1016/j.chaos.2007.06.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907003852
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.06.014?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. El Naschie, M.S., 2006. "Superstring theory: What it cannot do but E-infinity could," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 65-68.
    2. Naschie, M.S. El, 2006. "Fractal black holes and information," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 23-35.
    3. Andres, Jan & Fišer, Jiří & Gabor, Grzegorz & Leśniak, Krzysztof, 2005. "Multivalued fractals," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 665-700.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Thangaraj, C. & Easwaramoorthy, D. & Selmi, Bilel & Chamola, Bhagwati Prasad, 2024. "Generation of fractals via iterated function system of Kannan contractions in controlled metric space," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 188-198.
    2. Ullah, Kifayat & Katiyar, S.K., 2023. "Generalized G-Hausdorff space and applications in fractals," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Andres, Jan & Rypka, Miroslav, 2013. "Dimension of hyperfractals," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 146-154.
    4. 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).
    5. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. Prithvi, B.V. & Katiyar, S.K., 2022. "Interpolative operators: Fractal to multivalued fractal," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. 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.

    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. Zhang, Yongping & Sun, Weihua & Liu, Shutang, 2009. "Control of generalized Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1738-1744.
    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. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and characterizations of orthogonal vector-valued multivariate wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1835-1844.
    4. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    5. Murdzek, R., 2007. "A direct link between large-scale structure and cosmic strings," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 748-753.
    6. El Naschie, M.S., 2006. "On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 876-881.
    7. Yin, Xin-An & Yang, Xiao-Hua & Yang, Zhi-Feng, 2009. "Using the R/S method to determine the periodicity of time series," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 731-745.
    8. Chen, Ning & Hao, Ding & Tang, Ming, 2009. "Automatic generation of symmetric IFSs contracted in the hyperbolic plane," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 829-842.
    9. Chen, Qing-Jiang & Qu, Xiao-Gang, 2009. "Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1676-1683.
    10. Altun, Ishak & Sahin, Hakan & Aslantas, Mustafa, 2021. "A new approach to fractals via best proximity point," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    11. Thangaraj, C. & Easwaramoorthy, D. & Selmi, Bilel & Chamola, Bhagwati Prasad, 2024. "Generation of fractals via iterated function system of Kannan contractions in controlled metric space," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 188-198.
    12. Marek-Crnjac, L., 2006. "Pentaquarks and the mass spectrum of the elementary particles of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 332-341.
    13. Chiou, Juing-Shian & Cheng, Chun-Ming, 2009. "Stabilization analysis of the switched discrete-time systems using Lyapunov stability theorem and genetic algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 751-759.
    14. Singh, S.L. & Jain, Sarika & Mishra, S.N., 2009. "A new approach to superfractals," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3110-3120.
    15. Tanaka, Yosuke, 2007. "The mass spectrum of heavier hadrons and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 996-1007.
    16. Nozari, Kourosh & Mehdipour, S. Hamid, 2009. "Failure of standard thermodynamics in planck scale black hole system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 956-970.
    17. Gottlieb, I. & Agop, M., 2007. "El Naschie’s ε(∞) theory and an alternative to gauged spacetime scale relativity theory," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1025-1029.
    18. Agop, M. & Enache, V., 2007. "Gauge theories on El Naschie’s ε(∞) space-time topology," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 296-301.
    19. El Naschie, Mohamed Saladin, 2006. "Is gravity less fundamental than elementary particles theory? Critical remarks on holography and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 803-807.
    20. El Naschie, M.S., 2008. "High energy physics and the standard model from the exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 1-17.

    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:39:y:2009:i:3:p:1224-1231. 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.