IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i1p24-32.html
   My bibliography  Save this article

Cumulative growth with fibonacci approach, golden section and physics

Author

Listed:
  • Büyükkılıç, F.
  • Demirhan, D.

Abstract

In this study, a physical quantity belonging to a physical system in its stages of orientation towards growth has been formulated using Fibonacci recurrence approximation. Fibonacci p-numbers emerging in this process have been expressed as a power law for the first time as far as we are aware. The golden sections τp are related to the growth percent rates λp. With this mechanism, the physical origins of the mathematical forms of eq(x) and lnq(x) encountered in Tsallis thermostatistics have been clarified. It has been established that Fibonacci p-numbers could be taken as elements of generalized random Cantor set. The golden section random cantor set is used by M.S. El Naschie in his fundamental works in high energy physics and is also considered in the present work. Moreover, we conclude that the cumulative growth mechanism conveys the consequences of the discrete structure of space and memory effect.

Suggested Citation

  • Büyükkılıç, F. & Demirhan, D., 2009. "Cumulative growth with fibonacci approach, golden section and physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 24-32.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:24-32
    DOI: 10.1016/j.chaos.2008.10.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908004876
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.10.023?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. Stakhov, Alexey & Rozin, Boris, 2006. "The continuous functions for the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1014-1025.
    2. Stakhov, Alexey, 2006. "The golden section, secrets of the Egyptian civilization and harmony mathematics," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 490-505.
    3. Marek-Crnjac, L., 2006. "The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1113-1118.
    4. Marek-Crnjac, L., 2007. "Fuzzy Kähler manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 677-681.
    5. El Naschie, M.S., 2006. "Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 297-330.
    6. Stakhov, Alexey, 2006. "Fundamentals of a new kind of mathematics based on the Golden Section," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1124-1146.
    7. He, Ji-Huan & Xu, Lan, 2009. "Number of elementary particles using exceptional Lie symmetry groups hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2119-2124.
    8. Marek-Crnjac, L., 2007. "Higher dimensional dodecahedra as models of the macro and micro universe in E-infinity Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 944-950.
    9. Stakhov, A.P., 2005. "The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 263-289.
    10. El Naschie, M.S., 2008. "String theory, exceptional Lie groups hierarchy and the structural constant of the universe," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 7-12.
    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. Buyukkilic, F. & Ok Bayrakdar, Z. & Demirhan, D., 2015. "Investigation of cumulative growth process via Fibonacci method and fractional calculus," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 237-244.
    2. Adam, Maria & Assimakis, Nicholas & Farina, Alfonso, 2015. "Golden section, Fibonacci sequence and the time invariant Kalman and Lainiotis filters," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 817-831.
    3. Fiorenza, Alberto & Vincenzi, Giovanni, 2011. "Limit of ratio of consecutive terms for general order-k linear homogeneous recurrences with constant coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 145-152.

    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. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    2. Stakhov, Alexey, 2007. "The generalized golden proportions, a new theory of real numbers, and ternary mirror-symmetrical arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 315-334.
    3. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    4. Kocer, E. Gokcen & Tuglu, Naim & Stakhov, Alexey, 2009. "On the m-extension of the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1890-1906.
    5. Stakhov, Alexey & Rozin, Boris, 2007. "The “golden” hyperbolic models of Universe," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 159-171.
    6. Buyukkilic, F. & Ok Bayrakdar, Z. & Demirhan, D., 2015. "Investigation of cumulative growth process via Fibonacci method and fractional calculus," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 237-244.
    7. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    8. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.
    9. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.
    10. Marek-Crnjac, L., 2008. "Exceptional and semi simple Lie groups hierarchies and the maximum number of elementary particles beyond the standard model of high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 1-5.
    11. Stakhov, A.P., 2007. "The “golden” matrices and a new kind of cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1138-1146.
    12. Stakhov, Alexey, 2006. "The golden section, secrets of the Egyptian civilization and harmony mathematics," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 490-505.
    13. Kılıç, Emrah, 2009. "The generalized Pell (p,i)-numbers and their Binet formulas, combinatorial representations, sums," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2047-2063.
    14. Kilic, E. & Stakhov, A.P., 2009. "On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2210-2221.
    15. Marek-Crnjac, L., 2009. "A short history of fractal-Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2697-2705.
    16. El Naschie, M.S., 2006. "An elementary proof for the nine missing particles of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1136-1138.
    17. El Naschie, M.S., 2006. "Is Einstein’s general field equation more fundamental than quantum field theory and particle physics?," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 525-531.
    18. 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.
    19. El-Okaby, Ayman A., 2008. "Exceptional Lie groups, E-infinity theory and Higgs Boson," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1305-1317.
    20. Crasmareanu, Mircea & Hreţcanu, Cristina-Elena, 2008. "Golden differential geometry," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1229-1238.

    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:42:y:2009:i:1:p:24-32. 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.