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Introduction of H2O2 into bicarbonate aqueous solutions (BAS) initiates the development of redox processes in them, accompanied by a gradually increasing photons emission (PE), which does not quench for many months. In a set of identical samples taken from one portion of the activated BAS, a nontrivial dynamics of change in the "scatter of results" is observed. Immediately after sampling from a portion of the BAS, the standard deviation from the mean value of the PE intensity in various samples is relatively small, after a few days it increases many times, and then the differences between "parallel samples" begin to smooth out, and the standard deviation decreases significantly. The "scatter of data" is caused not by a smooth, but by a clearly pronounced discrete nature of the distribution of results, by the presence of "allowed" and "forbidden" nonequilibrium states in the BAS. The processes taking place in the BAS exhibit the features of "deterministic chaos" tending to a certain attractor. Developing biological systems behave in a similar way. This phenomenon has the signs of "equifinality", a characteristic property of biological systems, which, starting from one initial state, then move along diverging trajectories, but then begin to "strive" to the same state for all. It is noteworthy that this property is characteristic of the activated BAS, which in a sense is a prototype of living systems.