Insertion of H2O2 into bicarbonate aqueous solutions (BAS) initiates the development of redox processes in them accompanied with gradually increasing photon emission (PE) that does not disappear for many months. We report here of the non-trivial changes of “data scattering” of PE intensity measured in a set of identical probes of activated BAS obtained from one common sample of BAS. Immediately after taking aliquots from the original BAS standard deviation of the mean PE intensity from different test tubes does not exceed 5-6%, but within several days it increases dramatically reaching 50-70% of the mean at the stage of maximal rate of PE growth from activated BAS samples. «Data scattering» is caused by discrete character of distribution of the results, by the existence of “allowed” and “forbidden” non-equilibrium states if activated BAS. After reaching maximal values “data scattering” begins to decline reaching within several weeks 10-20% of the mean. Processes occurring in BAS exhibit features of the "deterministic chaos", aspiring to a certain attractor. There are certain similarities in the behavior of activated BAS and developing biological systems. The phenomenon has signs of "equifinality", namely, the property of biological systems that start their development from very similar initial state begin then moving on divergent paths, but later tend to to "strive" to the state similar for all the developing individuals. It is noteworthy that this property is characteristic of activated BAS, which in a certain sense, is the prototype of living systems.