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

TL;DR

This paper explores a specific mathematical function that, with appropriate parameters, can generate sequences exhibiting unpredictable and random-like behavior, useful for applications requiring randomness.

Contribution

It introduces a novel mathematical function and demonstrates its potential to produce unpredictable sequences through classical analysis tools.

Findings

The function can generate sequences with unpredictable dynamics.

Proper parameter choices lead to sequences passing randomness tests.

The method offers a new approach for pseudo-random number generation.

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.