Statistical Complexity in Traveling Densities

TL;DR

This paper investigates how statistical complexity varies when two identical traveling densities, such as Gaussian, rectangular, and triangular, cross each other, revealing the density shapes that maximize complexity.

Contribution

It provides a detailed analysis of the behavior of statistical complexity during the crossing of different traveling densities, identifying shapes with extreme complexity values.

Findings

Gaussian densities exhibit a maximum complexity at crossing

Rectangular densities show a distinct complexity peak during crossing

Triangular densities have a characteristic complexity behavior during crossing

Abstract

In this work, we analyze the behavior of statistical complexity in several systems where two identical densities that travel in opposite direction cross each other. The crossing between two Gaussian, rectangular and triangular densities is studied in detail. For these three cases, the shape of the total density presenting an extreme value in complexity is found.