Emergence, Locating and Measuring It - Systematic Design for Emergence in Cellular Nonlinear Networks - page 71

Fig. 4.13. Distributions of the clustering coefficient Clus for various families of semitotalistic
cellular automata with 2D neighborhoods ( left column ) and 1D neighborhoods ( right column ).
The horizontal axis plots the value of Clus while the vertical axis plots the fraction of CA
from the family exhibiting a certain Clus value

(a) Var - In this case, for most of the CA family members, there is a simple

dynamics, typically characterized by a small transient time followed by a perma-
nent regime exhibiting a low periodicity or a steady state.
(b)

v

v - In this case, quite frequently the CA behaves as a “noise gen-
erator”, with a quality of noise to be more precisely defined by the magnitude of
the clustering coefficient Clus . Most of the CAs in this category, namely those
with

1 Var v 2

Clus are the “good” (white noise) random number generators, but many
other noise generators (pink, or blue) could be found within this category as well.
Typically for CAs in this category there are neither long transients, nor gliders.

# 0

(c) v 2 - This case (with a relatively small fraction of the entire population)

is the most interesting for complexity, since here it is likely to find gliders and
long transients. Note that in some cases, where the finite running time cannot re-
veal long transients (e.g. ID=404 in Fig. 4.11), the variance parameter is the only

Var

capable to indicate the presence of a complex behavior.

As seen in Fig. 4.15 the distribution of the scaled transient length Tran is also
less dependent on the type of cell and topology. Moreover, one cannot easily iden-
tify a bifurcation parameter like in the case of the previous two parameters. This
indicates that the transient length is less important as a qualitative measure but
rather as an additional check-up applied to qualitative behaviors indicated by the
two other measures of complexity. Based more on experiments and less on the
structure of the distribution, a quantitative bifurcation parameter t1 (ranging from