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0.8
0.6
0.4
0.2
0.0
0
2000
4000
6000
8000
10000
t
Fig.10.
The time series of the concentration for rule
φ
c
starting from a random initial
concentration of 0
.
5. It can be observed that the quasiperiodic regimen is metastable.
Lattice size is 2000 cells.
use the tools of the “computational mechanics” developed by Crutchfield and
Hanson [6]. This point of view describes the computation embedded in the CA
space-time configuration in terms of domains, defects and defect interactions.
Here we describe two of the best evolved rules:
φ
a
and
φ
c
. Figure 11-a shows a
space-time diagram of rule
φ
a
. Time starts on
t
= 0 and goes from up down and
space is displayed on the horizontal axis. Figure 11-a shows patterns in which
there is an easily recognized spatio-temporally periodic background -the domain-
on which some dislocations move. In the simplest case a domain consist of a set
of cells in the space-time diagram that are always repeated; for example, the
domain for rule
φ
a
is shown in Table 2. If over a long time all the cells of the
space-time diagram are in the domain then the concentration of activated cells
will be oscillating among three values 1
/
2, 1
/
3 and 1
/
6. Displacements of the
domain shown in Table 2 along the temporal axis give place to other domains
and then at the boundaries between them there are some defects cells. For rule
φ
a
these defects cells are spatially localized and time-invariant and they are
considered to be “particles”.
Table 2.
Domain for rule
φ
a
.
110100
110000
010000
100110
000110
000010