  Previous study of cellular automata and random Boolean networks has shown
emergent behavior occurring at the edge of chaos where the randomness
(disorder) of internal connections is set to an intermediate critical value.
The value at which maximal emergent behavior occurs has been observed to be
inversely related to the total number of interconnected elements, the
neighborhood size. However, different equations predict different values. This
paper presents a study of one-dimensional cellular automata (1DCA) verifying
the general relationship but finding a more precise correlation with the radius
of the neighborhood rather than neighborhood size. Furthermore, the critical
value of the emergent regime is observed to be very close to 1/e hinting at the
discovery of a fundamental characteristic of emergent systems.
