Cumulative growth with fibonacci approach, golden section and physics

• Published in: Chaos, solitons and fractals solitons and fractals, 2009-10, Vol.42 (1), p.24-32
• Main Authors: Büyükkılıç, F., Demirhan, D.
• Format: Article
• Language: English
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2008.10.023

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 τ p are related to the growth percent rates λ p . With this mechanism, the physical origins of the mathematical forms of e q ( x) and ln q ( 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.