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Cumulative growth with fibonacci approach, golden section and physics

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  • 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
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    References listed on IDEAS

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    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.
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    5. 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.
    6. Stakhov, Alexey, 2006. "The golden section, secrets of the Egyptian civilization and harmony mathematics," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 490-505.
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    9. 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.
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    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.

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