![](bg6.png)
Rule φ
c
also has a periodic background that fulfils the
requirements of having a period-3 oscillating concen-
tration, but the main difference with φ
a
and φ
b
is the
way the global coordination is acquired. The defect
cells for rule φ
c
are irregular propagating structures,
which is a characteristic of rules that belong to the IV
Wolfram’s class. And finally are the patterns gener-
ated by the rule φ
d
where there is a lack of regularity
or periodic background. While rules φ
a
, φ
b
and φ
c
evolve towards a final state in which the concentra-
tion reaches a well determined three state, the three
values of the concentration for rule φ
d
show a noisy
behavior ( Figure 3d). Rule φ
d
is a chaotic rule and its
behavior may be interesting from an statistical point
of view, though this is out of the scope of this work.
Table 2: Domain for rule φ
b
and the concentration.
Space
1 1 0 1 0 0 c
1
= 1/2
T 1 1 0 0 0 0 c
2
= 1/3
i 0 1 0 0 0 0 c
3
= 1/6
m 1 0 0 1 1 0 c
1
= 1/2
e 0 0 0 1 1 0 c
2
= 1/3
0 0 0 0 1 0 c
3
= 1/6
5 CONCLUSIONS
The study of non trivial collective behavior in CA
has suggested a new computational task like the P3
task. A genetic algorithm, with the appropriate fitness
function, has been able to find answer rules that have
regular repeating space-time configurations. These
rules, belonging to the Wolfram’s class II, attained the
global coordination among the entire lattice cells with
propagating structures –particles– that interact among
them until a regular and final state is reached. In
the patterns generated by these rules it can be distin-
guished domains and particles like in the density and
the synchronization tasks. And the global coordina-
tion can be explained using the tools of the “computa-
tional mechanics” originally developed by the EVCA
group of Crutchfield and Mitchell.
But our GA has also found some rules ( class III
and IV ) for which the space-time diagrams do not
show a regular pattern. The emergence of a global
computation by these chaotic and complex rules is
very interesting and points out the existence of other
synchronization strategies not well understood yet.
We think that many of the results obtained in tasks
like this one can provide a useful information to es-
tablish a more general framework to study the emer-
gence of global coordination in one dimensional CA.
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