Natural Computing Paradigms and Emergent Computation - Systematic Design for Emergence in Cellular Nonlinear Networks - page 6

emergence will be introduced in Chap. 4. Their common feature is that they are
experimental, i.e. they require a simulation of the CA with some conveniently
chosen initial state and number of cells during a convenient number of iterations.
Although the choices of these “convenient” CA parameters induces a degree of
uncertainty in these measures, they are extremely useful for a better understanding
of emergence and its relationship with the cell structure. They also provide useful
hints on how to tune these measures in order to select only CA genes giving a de-
sired behavior. In fact this process of tuning and selection is further detailed
in Chap. 6 where it is referred as a sieving process. Sieving with experimental
measures of emergence require that a table with this measures is available and
computed previously for all cells within the family. Chapter 5 is devoted to one
additional measure, the exponent of growth, which provides novel information
in addition to those defined previously in Chap. 4. The exponent of growth turns
out to have a good predictive power for emergent properties, and although it is
experimentally defined in Chap. 5, it turns out later in Chap. 7 that is the only
among all measures for emergence that can be also analytically determined solely
based on cells structure and its neighborhood. Therefore, the theory of probabil-
istic exponent of growth in Chap. 7 represents a step ahead towards the “holly
grail” of emergence, i.e. predicting the behavior without a need to simulate the
system. Information theory and the view of cells as nonlinear functions plays es-
sential role in structuring this theory. Several examples of applying this theory,
and comparisons with the experimental counterpart of the same measure confirm
its validity and predictive power. It is particularly worth applicable for huge fami-
lies of cells where the time to determine the measures experimentally for the entire
family o cells is prohibitive. Instead, the hints given by the theory of probabilistic
exponent of grow allows a clever design instead, where the result is simply a set of
inequalities with variables drawn from the bits defining the cells gene.
The last chapter provides three innovative applications of cellular computing
systems in problems such as pattern recognition and lossy image compression to
exemplify the potential of the design for emergence tools described in this topic.