International Encyclopedia of Systems and Cybernetics

The limit under which a process cannot propagate itself in a medium or an almost homogeneous system or, on the contrary, beyond which it propagates without limits.

This threshold, which is expressed by a %,depends on the spatial arrangement of the elements. P. GRASSBERGER, using the very simple example of a bicolor net of square components, shows that the percolation threshold is theoretically at 59,29% When this limit is reached, percolation triggers and isolated clusters of the most numerous components percolate, i.e. become interconnected and invade the near totality of the surface, confining in turn the less numerous components into small clusters isolated from each other (1991, p.649).

In this way, for example, epidemics become pandemics.

The existence of percolation thresholds explains the better stability of very heterogeneous systems as, for example, the natural ecological systems differentiated in very numerous niches corresponding to many species.

GRASSBERGER, moreover, points out that "… in the vicinity of a percolation threshold, the behavioral diferences between various systems become blurred and all show a truly universal behavior Their properties do not anymore depend on their particular structure but on the contrary, obey to global laws called "scale laws". However, while this universality is now well confirmed, a complete mathematical formulation is still lacking. It is not always evident… how to distinguish from the start which are the universal magnitudes and which are the details of the structure which should be neglected" (p.642).