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6.3 Examples and Applications of the Double Sieve
Method
Following the above methodology is now possible to define various types of
sieves, all associated with a certain “A” statement.
6.3.1 Intelligent Life Behaviors and Uncertainty in Using Sieves
In Chap. 5, with the introduction of the exponent of growth
U
as a fourth measure of
complexity, it was revealed that CA behaviors characterized by a slow growth
near the edge between “explosive” and “implosive” behaviors are likely to model
real-life biological processes characterized by a tamed tendency of growth, when
starting from a specified initial state spatial cluster.
Let define a first sieve as
>
@
2
P
U
exp
10
U
2
to favor those behaviors
1
characterized by a small exponent of growth
0
U
. Since in Chap. 4 we
discovered that complex behaviors are typically associated with a large variance
(much larger than the bifurcation parameter
v2
) it would be reasonable to add
a second sieve to select only those cells giving large variances when connected
into the specified cellular structure. This second sieve is defined as
2
.
>
@
P
favoring only those cells with a variance
larger than 0.12 (while the bifurcation parameter
v2
= 0.07 in the case of “2s9”
family). As seen in Chap. 5, for this family there is a large number of cells with
“slow growth” therefore there is a rich basis of selection.
The global sieve is now defined as a fuzzy AND between the two previously
defined sieves and therefore:
Var
0
.
0
.
tanh
10
Var
0
.
12
2
>
@
. Choosing a truth
P
U
,
Var
min
P
U
,
P
Var
A
A
1
A
2
threshold
T
results in the following list of IDs: 3987, 6344, 55999, 108584,
242589, 243504, 244126 from the “2s9” family.
Simulating and observing the dynamical evolution of the corresponding cellular
automata reveals common features that can be linguistically described in the
“fuzzy” statement “A”. In all cases simulations were done in a 100×100 array with
a random initial state. The evolution of CA with ID = 3987 is shown in Fig. 6.2
for up to 6,000 iterations. There are several extremely interesting features:
(a)
0
Just like in the “Game of Life”, several types of gliders emerge and interact
forming slowly varying patterns reminiscent of biological dynamics. As in
the “game of life” further detailed analysis of those gliders and their inter-
actions may reveal interesting properties that could be used to prove such
properties as universal computation.
(b)
Unlike in the “Game of Life” where there is a global tendency towards an
ordered global state (after several thousands of iterations the system usually
enters a low period or steady state), here the dynamics seems to be eter-
nal. Often intelligence is related to a capacity of adapting to an environ-
ment such that there is a perpetual survival (event though some structures
vanishes, they are replaced with some similar other). Therefore in the next
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