sin[n Delta t sin (n Delta t1)] as a source of unpredictable dynamics

Abstract

We investigate the ability of the function sin[n Delta t sin (n Delta t1)], where n is an integer and growing number, to produce unpredictable sequences of numbers. Classical mathematical tools for distinguishing periodic from chaotic or random behaviour, such as sensitivity to the initial conditions, Fourier analysis, and autocorrelation are used. Moreover, the function acos{sin[n Delta t sin (n Delta t1)]}/pigreek is introduced to have an uniform density of numbers in the interval [0,1], so it can be submitted to a battery of widely used tests for random number generators. All these tools show that a proper choice of Delta t and Delta t1, can produce a sequence of numbers behaving as unpredictable dynamics.