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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
 
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