Visualization of the Signals Entropy Structure Based on Walsh–Hadamard Functions

Abstract

New molecular genetic algorithms, as tools for the visualization and analysis of big data, have made it possible not only to illustrate the internal structure of DNA molecules within their parameters but also to explore the field of chaos theory, particularly to display processes and signals close to chaotic ones. This provides a new perspective on the problem of determining criteria for borderline states between order and chaos. This article demonstrates the differences between chaotic and quasi-chaotic signals when visualized with molecular genetic algorithms. It presents examples of molecular genetic mappings of signals generated using various pseudorandom noise generators, as well as acoustic signals. This article considers structural and integral (folded) mappings as one-dimensional and two-dimensional projections of the pattern. The authors illustrate the internal structure of the reconstructed signal mappings in spaces of fractional dimensionality, which is considered as a visualization of the entropy structure based on functional mappings in spaces of the fractional dimension. As a result of this research, it was found that the use of molecular genetic algorithms for visualizing information signals makes it possible to identify the so-called entropy structure of these signals. At the same time, the entropy structure of chaotic signals is absent.