Predicting Emergence from Cell’s Structure - Systematic Design for Emergence in Cellular Nonlinear Networks - page 113

1s5 Column=[4 7 2 1 6] Line=[3 8 9 10 5] P i , j =Clus 1s5 Column=[4 7 2 1 6] Line=[3 8 9 10 5] P i , j =Clus

5 5

10 10

15 15

20 20

25 25

30 30

5 10 15 20 25 30 5 10 15 20 25 30

Fig. 7.3. Parametrizations of the same cells in different connectivity. Left : one-dimensional
CA (1s5); Right : two-dimensional CA (2s5). Note some general similarity (as imposed by

solely the cell's structure) but also some differences (effects of the connectivity)

Parametrizations are also useful tools to compare among the same families of
cells when put into different interconnectivities. This is the case with the 1s5 and
2s5 CA families. In the first case, the grid topology is one-dimensional while in
the second case the interconnectivity is two-dimensional. Using the same “good”
parametrization as in Fig. 7.2 one can observe differences and similarities in
Fig. 7.3. It is interesting to observe a global similarity (given by the cell structure)
but also some differences explained by the different neighborhood connectivity.
More in-depth study is needed to refine an analytical model to include rigorously
both effects, but nevertheless the parametrization is a good preliminary tool to be
used as a starting point for such an analysis.
A “good” parametrization has another practical use: If the emergence measure
assigned to

P , has a certain meaning (e.g. as obtained from the sieving process)
the parametrization will group cells giving similar emergent behaviors in a topo-
logically connected region within the parametrization. Therefore once we have de-
tected an “interesting” behavior it is easy to identify other cells having the same
behavior by simply looking around in the graphical representation of a “good” pa-
rametrization. As an example, consider a detail from a random parametrization of
the 2s9 family, represented in Fig. 7.4.
The quality measured here is the transient length (larger for interesting, com-
plex behaviors, represented here with darker colors). The well known Game of

j

Life (ID=6152) can be easily identified within the entire parametrization. But

looking globally at the parametrization reveals some similar neighbours with the
same quality (the black strip down to the location of “Life”). Several IDs from this
strip can be easily determined once we know the parametrization. A short list in-
cludes ID = 6,216, 6,280, 6,664, 6,600. They differ from the original gene of
“Life” by mutations in any of the bits 6-9 of the original ID (here the less signifi-
cant bit is denoted zeroth bit). Running their associated CAs reveals that the emer-
gent behavior is very similar to the Game of Life, thus confirming the predictive
power of a parametrization for cells within a small neighborhood and with the
same value of the measured emergence quality.