Calculating the complexity of spatially distributed physical quantities

Abstract

With the development of mathematics as well as natural sciences and with the improvement of the human cognitive level, a new discipline dealing with complexity of different and complex natural systems has been recognized. Therefore, several complexity measures have been developed. Complexity measures provided to scientific community new insights into environmental processes that cannot be discovered by the traditional mathematical methods. Spatial distribution of heavy metals and radionuclides (HM&RN further) is formed by acting natural processes as well as human activities. Despite the fact that this distribution plays an important role in environmental processes, it has not been analyzed with deserving attention. The usual way to present the results obtained by some measurements having an objective to describe environmental properties is by creating a map of spatial distributions of some chosen quantities or indices. Attempts to introduce some quantitative measure, which characterizes measured areal distribution (and corresponding map) of physical quantity, cannot be frequently encountered in scientific community. In this paper, we invested an effort to introduce some numerical indices as a new measure which can describe spatial distributions of physical quantity based on the complexity computed by the Lempel–Ziv algorithm (LZA) or Lempel–Ziv complexity (LZC).