Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored. This paper aims to be a complete guideline of the theory and application of the algorithms, intended to explain their characteristics in detail to researchers from different fields. While initially developed for physiological applications, both algorithms have been used in other fields such as medicine, telecommunications, economics or Earth sciences. In this paper, we explain the theoretical aspects involving Information Theory and Chaos Theory, provide simple source codes for their computation, and illustrate the techniques with a step by step example of how to use the algorithms properly. This paper is not intended to be an exhaustive review of all previous applications of the algorithms but rather a comprehensive tutorial where no previous knowledge is required to understand the methodology.

It is commonly accepted that the evolution of the human eye has been driven by the maximum intensity of the radiation emitted by the Sun. However, the interpretation of the surrounding environment is constrained not only by the amount of energy received but also by the information content of the radiation. Information is related to entropy rather than energy. The human brain follows Bayesian statistical inference for the interpretation of visual space. The maximization of information occurs in the process of maximizing the entropy. Here, we show that the photopic and scotopic vision absorption peaks in humans are determined not only by the intensity but also by the entropy of radiation. We suggest that through the course of evolution, the human eye has not adapted only to the maximum intensity or to the maximum information but to the optimal wavelength for obtaining information. On Earth, the optimal wavelengths for photopic and scotopic vision are 555 nm and 508 nm, respectively, as inferred experimentally. These optimal wavelengths are determined by the temperature of the star (in this case, the Sun) and by the atmospheric composition.