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Fig. 4.12.
Profile of the CA family “1s7”. Note similarities with the profiles obtained for
other semitotalistic cells. Note a similar fraction of the cells exhibiting complexity, though
giving a larger variety of behaviors because of the large number of cells within the entire
family
those with “random” behaviors (with
) and those with “ordered” or
Clus
|
0
“near ordered” behavior (with
Clus
), in the case of 1D topologies (even in the
case of using the same cell, as in the case of 1s5 vs. 2s5 families), the clustering
coefficient is widely distributed without a clear preference for a maximum in the
middle. The “ordered” CAs with
|
1
Clus
are predominant in such cases. As a
practical conclusion, while it is known that good “random” sequence generators
require
|
1
Clus
,
it is clear that such “random” generators are much easily to be
found from a population of CA with cells distributed over a 2D grid. On the other
hand, for those applications where a wide range of
Clus
values are needed, a better
choice is a 1D-neighborhood.
Such distributions, particularly those drawn from cellular automata with 2D
neighborhoods, can be characterized by certain scalar features, called
c1
and
c2
in
our example. Such scalar values indicate
bifurcation points
with respect to qualita-
tive behaviors of the CA. Here they are defined as points of reaching a minimum
in the distribution. As seen later in Chap. 6, they can be effectively used in defin-
ing various “sieves”.
The distribution of the
Var
complexity measure is plotted in Fig. 4.14. Note
that in this case the topology (1D or 2D)
plays no significant role
and does not in-
fluence the unique shape of distribution which always has two peaks. Like in the
previous case, two scalar values
v1
and
v2
may be introduced to define the major
features of the distribution. These values are influence by both the topology (1D or
2D) and the cell type, as seen from the plots. A detailed analysis of various CA
exhibiting different
Var
values revealed that
v1
and
v2
separates between three
qualitatively different classes of behaviors:
|
0
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