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The research is aimed at studying the quantitative laws of the morphological pattern dynamics for alluvial plains. Basing on the random process theory - the renewal process theory, we substantiate that in the course of the development despite constant changes such as generating new packages, erasing old packages, changing of the number of a package, some features of the morphological pattern remain the same. They are the length distribution of the arrows for the preserved (non-erased) package fragments, the durati...