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//***aaaaaa**aaaaaaaaa+*+100100Q1+110110+00Q11100,1-[8,09] = 6
*Q*/*aaaaaaQaa+-aaaaaaQ+-101110+-Q/10001//QQ00010,0-[9,00] = 6
As their expression shows, they also are exact formulations of Kepler's Third
Law. Consider, for instance, the perfect solution discovered in generation 3
of run 3. It encodes the following expression (the contribution of each ADF
is shown in brackets):
(
a
)
3
P
a
(6.4)
(
a
)
(
a
2
)
and, therefore, is also a perfect formulation of Kepler's Third Law.
6.4 RNCs and the Cellular System
The complexity of both the uni- and multicellular systems is considerably
higher than that of the acellular systems we have dealt with so far. And since
this complexity was not something created naturally by the system itself, it is
important to know how plastic these systems are, or in other words, how
efficient is evolution in these systems.
We have seen already in the previous section that, at least for simple prob-
lems, the cellular system is extremely flexible and allows an efficient evolu-
tion. This gives hope that perhaps it is possible to increase the complexity of
the cellular system even more in order to introduce new features, such as a
facility for handling random numerical constants.
The analog circuit we are going to design in this section with the cellular
system is the same of section 5.6.5 and, from the results obtained in that
section, we know that random numerical constants are absolutely necessary
to design this particular circuit. Thus, in this section, we are going to see first
how random numerical constants are implemented in the cellular system and
then proceed with the testing of this new algorithm on this challenging prob-
lem of analog circuit design.
6.4.1 Incorporating RNCs in ADFs
The incorporation of random numerical constants in automatically defined
functions is not difficult. As you probably guessed, the gene structure used to
