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In social and biological systems, the realization that (dramatic) macroscopic events can be generated by chains of auto-catalytic elementary "microscopic" events emerges lately in its full power only after the macroscopic effects were experienced (for good of for bad) for many centuries.

The reaction (autocatalysis equation 1) leads naively to the differential equation  (malthus autocatalytic equation). However there are crucial corrections to this naïve translation. As discussed in the logistic equation section, the fact that there is a finite number of U-235 nuclei in the particular slob of material means that at some stage the probability to find a non-fisioned yet U-235 nucleus will decrease.

This is expressed by the saturation term in (Verhulst logistic eq.) . Moreover, the fact that the nuclei are placed in a particular spatial geometry means that it is important how many neutrons can move from one location (where they were generated) to another location (where to initiate a reaction). One can try to express it by differential equations of the type  (spatially distributed logistic) or (diff eq logistic system). However, this is not always correct. The long flights of the neutrons, the slowing down in various conditions, the change of reaction rate as a function of their speed may defy analytic solutions in many situations. Going back to the direct representation of the system in terms of its elementary agents is always a valid option and often the only one.

In fact some crucial effects are obtainable and in fact discernable only in this formalism.  In particular, the connection between the autocatalytic dynamics of the logistic systems and the emergence of power laws and of localized adaptive resilient collective objects is obtainable only when one takes into account the stochastic character related to the discrete (rather then continuum) texture of the U-235 material and of the other systems discussed below.

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