Golden ratio in science, as random sequence source, its computation and beyond
Computers & Mathematics with Applications
Golden ratio versus pi as random sequence sources for Monte Carlo integration
Mathematical and Computer Modelling: An International Journal
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Random Fibonacci sequences are stochastic versions of the classical Fibonacci sequence f"n"+"1=f"n+f"n"-"1 for n0, and f"0=f"1=1, obtained by randomizing one or both signs on the right side of the defining equation and/or adding a ''growth parameter.'' These sequences may be viewed as coming from a sequence of products of i.i.d. random matrices and their rate of growth measured by the associated Lyapunov exponent. Following the techniques presented by Embree and Trefethen in their numerical paper Embree and Trefethen (1999) [2], we study the behavior of the Lyapunov exponents as a function of the probability p of choosing + in the sign randomization.