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propagate in time, which gives the characteristic zebra-like patterns. These strips
are stable and propagate further to the right or to the left.
(a)
(b)
Fig.4.
Space-time diagrams for the best asynchronous rule found. The density
ρ
0
=
0
.
55 in both (a) and (b) and the initial state configuration is the same. The different
time evolution points out the stochasticity of the updating policy.
3.4 Scalability of Evolved Automata
It is interesting to study the behavior of the evolved density classification rules
as the number
n
of cells in the grid increases. If the solution is scalable then,
as
n
increases, performances should remain more or less the same, although
the CA has been evolved for
n
= 149. Crutchfield and Mitchell [3] found that
their synchronous evolved CAs do not scale very well with the grid size, as their
performance decreases slightly when
n
goes from 149 to 599, and to 999. We have
found that the behavior of the best evolved asynchronous CAs are less influenced
by the grid size than their synchronous counterparts. As an example, in figure 5
we plot the performance of the best evolved CA with the uniform update method
as a function of the density for three lattice sizes,
n
= 149
,
599
,
999.
It is apparent that the larger grid sizes have a smaller region of error, i.e.
the performance is better for a larger interval around
ρ
0
=0
.
5, except in the
immediate vicinity of 0
.
5, where the performance is slightly less. On the whole,
it is clear that the performance stays constant or even it increases slightly with
increasing grid size.
4The Effect of Noise
There are at least two possible sources of indeterminism in CAs: the first is
random asynchronous updating, as explained in the previous sections; the second
