Apply of Graph Extension Function in Nature

Arbitrary systems will it be biological chemical physical cybernetical etc. may be described by a mathematical function namely by a graph extension function which we also call hierarchical function (and which mathematically shows hierarchical nature of science). This function can be also used to describe mathematical objects themselves which in the paper is shown on the example of the action of the graph extension function on the set of integers. A new theory of graph extensions similar to group extension theory is outlined. A theorem about the equivalence of different extension functions is proved. There exists an isomorphism between the modified functional graph of the cell (functional block-scheme) and the morphological graph of the cell (the graph expressing topological membrane intertransformations of the cell) which expresses the most essential features of for the biology of the cell and captures one of the specific differences between living and non-living systems. It is shown that the construction of the graph of a complex organism from the primordial graph given by Rashevsky is nothing but an extension of the primordial graph by the graph extension.