Emergence, Locating and Measuring It - Systematic Design for Emergence in Cellular Nonlinear Networks - page 55

Fig. 4.6. A longer simulation of CA with ID = 684 indicates that it has a behavior which
can be actually classified in Class II. Nevertheless, the long transient introduced here as an
emergence measure clearly indicates a complex dynamics having all features of a computa-
tional process: interaction of gliders, and halting after 2,355 iterations in this case. The
lower graph indicates the evolution of the clustering coefficient used to detect the transient
time
Note that for the other two examples in Class IV, we were not able to find the
halting moment but this does not mean it does not exist. It is only the limit we can
afford to do the simulation which impedes on finding large values of halting mo-
ments.
So far, a conclusion is that simple visual classification schemes as the one pro-
posed by Wolfram, although useful as a fist attempt to quantify emergence, are not
suitable for an in-depth analysis, particularly when it should be done automatically
by a computer program. Instead, numerical values (also called measure of emer-
gence) should be defined, to capture more precisely the quality of the nonlinear
dynamics in a cellular system. These measures were briefly introduced above but
their accurate definitions and computing algorithms will be detailed next. Later we
will show that Wolfram classes do exist and still have their relevance but as
partially overlapping sub-domains in a space defined by the newly introduced
measures of emergence.