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3.3 Initial Configurations
The very concept of emergence [19] asks for a separation of levels with different
entities and relationships, but according to the same laws. In our case it is essential to
define which is the situation that corresponds to the pre-replication level and what are
the entities that constitute it. Ultimately we have to define a class of cellular
landscapes from which replicators are intended to emerge.
A sort of random distribution of cell-states accommodates well with this idea of a
previous level in which there are no traces of organized patterns. However, this choice
is not practical due to time limitations. So, we have adopted similar criteria as other
structure-emergence testing systems like Venus [20], in the sense that the initial
configuration state distribution will be biased to favor the affinity of structural states.
To do so we consider a scale of distances from 1 to 5. For each pair of states
(i,j)
we define five affinity factors
A(i,j,d)
, one for each distance
d
, that will be used in
determining the probability of a particular arrangement of states in the pseudorandom
initial configuration. The value
A(i,j,d)
indicates how a cell in state
i
can influence the
probability that a cell at distance
d
is in state
j
. It can be positive or negative,
indicating affinity or repulsion between states. The interpretation of the distance scale
can be seen in the grid of table 1.
Table 1.
Distance grid for a particular cell.
5
4
3
4
5
4
2
1
2
4
3
1
0
1
3
4
2
1
2
4
5
4
3
4
5
To generate an initial configuration the following process is carried on until all the
cells are defined (have an initial state):
1.
Choose randomly an undefined cell
c
2.
Select the 24 cells which are in the Moore neighborhood of
c
with radius 3.
3.
For each state
s
calculate
p(s)=
∈
4.
Choose the state
t
for cell
c
in a random way so that the probability that
t=s
is
proportional to
p(s)
(if
p(s)
is negative consider it as 0)
Note that in step 3 some cells in
N
will be undefined. This problem is overcome
defining affinity factors
A(u,s,d)
for the “undefined state”
u
. These special values
allow to modulate the global percentage of quiescent states in all the configuration, a
parameter that appears to be significant in the experimental results.
With this method some cell states tend to aggregate, and the structural ones have a
polymerizing effect (normally in chains no longer than 4 cells), which settle minimal
conditions for pattern emergence. An example of initial configuration is shown in
Figure 3.
A(state(c'
),
s,
distance(c
,
c'
)
)
c'
N
