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).

中文翻译：

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计算空间分布物理量的复杂度

随着数学和自然科学的发展，随着人类认知水平的提高，处理不同复杂自然系统的复杂性的新学科得到了认可。因此，已经开发了几种复杂性度量。复杂性测量为科学界提供了对传统数学方法无法发现的环境过程的新见解。重金属和放射性核素（进一步称为 HM&RN）的空间分布是通过作用于自然过程以及人类活动而形成的。尽管这种分布在环境过程中起着重要作用，但它并没有得到应有的关注。呈现通过一些具有描述环境特性的目标的测量获得的结果的常用方法是创建一些选定数量或指数的空间分布图。试图引入一些定量的度量来表征物理量的测量区域分布（和相应的地图），在科学界并不常见。在本文中，我们努力引入一些数值指标作为一种新的度量，它可以基于 Lempel-Ziv 算法 (LZA) 或 Lempel-Ziv 复杂度 (LZC) 计算的复杂度来描述物理量的空间分布。表征物理量的测量区域分布（和对应的地图），在科学界是不常见的。在本文中，我们努力引入一些数值指标作为一种新的度量，它可以基于 Lempel-Ziv 算法 (LZA) 或 Lempel-Ziv 复杂度 (LZC) 计算的复杂度来描述物理量的空间分布。表征物理量的测量区域分布（和对应的地图），在科学界是不常见的。在本文中，我们努力引入一些数值指标作为一种新的度量，它可以基于 Lempel-Ziv 算法 (LZA) 或 Lempel-Ziv 复杂度 (LZC) 计算的复杂度来描述物理量的空间分布。