The Lorenz chaotic system, statistical independence and sampling frequency

The goal of this paper is to investigate the possibility of obtaining statistically independent data by making use of the Lorenz chaotic system in a computationally-efficient manner. In order to research the statistical independence, we will make use of a spatial Chi Square test. Furthermore, we will also compare the independence results when using solution data from the Lorenz system of differential equations solved for different step sizes (sampling frequencies). The experimental results showed that for the Lorenz chaotic system a time difference of more than 30s is enough in order to collect statistically independent data independent of the sampling frequency used to solve the system.