Emergence, Locating and Measuring It - Systematic Design for Emergence in Cellular Nonlinear Networks - page 66

Fig. 4.8. The >

@

Ltr , plane as a tool to rapidly identify different types of global behavior.
Note than the boundaries between domains are rather fuzzy and not sharp as suggested by
the use of word “classes of behavior”. The dynamics of several 1D cellular automata are
used to exemplify the location of various behaviors on the plane. The ID coding is the one
proposed in this topic and it coincides with the one proposed by Wolfram in [55,56]

C

The plane may be divided into several sections although the borders are not as
sharp as indicated in the picture. On the middle (

Clus ) there is a strip
corresponding to the Class III of Wolfram. Here the length of the transient is less
interesting (due to large fluctuations it is imprecisely measured), but all CA within
this strip display the randomness associated with Class III. The CA with ID = 30
(reported to be used for the random number generator in Mathematica) belongs to
this strip. Above and below the strip, the length of the transient differentiates
among the left side (short transients, or Class I, and II) and the right side (long
transients, complex behaviors, i.e. Class IV).
Where exactly should be that border placed?
There is no precise answer but experiments suggest that taking the boundary on
the Ltr axis at

0 0 05

ln may be a good choice, consistent with experimental observa-
tions showing that transient times comparable with the number of cells are often
associated with the presence of gliders. In our case, for

N

cells, the bound-

N 100

ary is at

Ltr # 4

.

Our emergence measures allow to draw a portrait for an entire family of
cells while not discarding entirely the classification proposed by Wolfram.
They rather allow to see the subtle differences between genes otherwise
considered as belonging to the same class, thus resolving the uncertainty in
the proposed classification system, as observed by many authors.