Predicting Emergence from Cell’s Structure - Systematic Design for Emergence in Cellular Nonlinear Networks - page 128

Uncertainty profiles as tools to classify among emergent behaviors. In
estimating the growing or exploding emergent behaviors we used two
parameters ( ua and ue ) computed as linear combinations of the entire
uncertainty profile (all uncertainties for the next state cells). A finer
classification between behaviors may be however obtained by an in-
depth analysis of the uncertainty profile as a vector. Cell's ID with
similar uncertainty profile vectors exhibit similar emergent behaviors.
The number of possible such vector gives also an indication about the
diversity of possible emergent phenomena to be expected for a given
cell family and neighborhood. For instance, it is rather simple to ex-

(f)

plain why “ 2s5 ” CAs exhibit no gliders while “ 1s5 ” CA s do. The rea-
ue may have only two values (correspond- son, is that in the first case

ing to either implosion or fast explosion) while the connectivity in the

“ 1s5 ” case allows for a larger number of possible values of ue , some

of them (closer to but larger than 1) favoring complex behaviors such

as the presence of gliders. Using the same reasoning it follows that for

the same type of semi-totalistic cells the 1D CA will exhibit a larger

variety of emergent behaviors than its 2D counterpart. Moreover, the
larger is the neighborhood the larger will be the variety of emergent
behaviors observed.