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which stands for all the 15 transitions that would result from its expansion, that is to
say, from the systematic substitution of the variables by their possible values. Then,
we define a number of varsitions that are expanded by the system into individual
transitions. This process typically produces an important number of repeated
transitions (and occasionally conflicts due to cellular programming errors), that are
sieved in order to produce the final active transition set.
According to this, we have used 950 different varsitions in the basic rules for
reproduction, that have expanded to 1.502.197 individual transitions. After
eliminating all the repeated ones, the final number of active transitions was 636.067.
When the transition set has been modified to include robust behavior, the number
of relevant local configurations has raised as much as to produce over 30.000
varsitions, that rendered an expanded set of more than 120 million transitions.
Nevertheless, since a great amount of varsitions are generated automatically the
redundancy degree is higher, and so the final transition state is reduced to about 12
million. The size of the table has heavily conditioned the experimental work: in a
Pentium III at 450 MHz with 256 MB RAM we need more than half an hour to load
the table (and this process has to be done each time a modified table is compiled). The
execution itself is reasonably fast, but it needs 1.5 GB of virtual memory.
The robust set of rules does not only include appropriate transitions to make the
patterns more viable in a hazardous environment. Some reconstruction and
maintenance rules are also included to improve the stability of components that could
organize in order to form a reproducing pattern. An example of the action of these
rules is shown in Figure 2.
Fig. 2.
Example of the maintenance and reconstruction rules. At early stages the structural
components of the patterns present in the cellular space (as are small pieces of conducting
paths) usually are incomplete and contain errors. The rules can recover some of these small
errors. The
black triangle
serves as an absolute reference to see how a piece of nude path (fluid
without any sheath) is partially lost and partially recovered.
It is important to note that the maintenance and reconstruction rules do favor the
emergence of patterns, but can by no means assure it by themselves. Instead,
emergence only occurs as the result the interaction of the small components due to the
reproduction mechanisms that are present in the basic rule set. On the other hand, the
maintenance and reconstruction rules are operative during all the phases of the
cellular experiments, and also have influence in the way stable reproducers interact
among them and with the environment.
