Emergence, Locating and Measuring It - Systematic Design for Emergence in Cellular Nonlinear Networks - page 67

Fig. 4.9. Projection on the Ltr , for the 1,024 members of the 2t9 CA family. Note

that long transient behaviors in this case, correspond also to large values (close to 1) of the
clustering coefficient

Clus

As expected, the famous “110” CA (proved in [17] to be the simplest CA capa-
ble of universal computation and its 3 “relatives” (according to [76, 77]) with
ID = 124, 137 and 193 are located within the Class IV region of the plane, but
quite closely to the Class III strip. Indeed, gliders are present in such CAs but
within a rather “noisy” dynamics, typical for Class III. As seen later, the profile
for different families of CA is such that some individuals will be placed in the
Class IV region but closer to the Clus=1 boundary, indicating the presence of neat
gliders, not affected by noise. For instance, Fig. 4.9 presents the profile obtained
in the Ltr , plane for the 2t9 CA family (totalistic, two-dimensional with 9

cells in the neighborhood).
In addition to clarifying the origin of uncertainties in the classification scheme
proposed by Wolfram, the above measures of emergence bring several other im-
portant advantages:

Clus

x One may easily do a statistics on a large family of cells, inferring relationships
such as the probability that a certain kind of behavior will occur in a family or
another (e.g. 1s5 or 1s9).