Emergence, Locating and Measuring It - Systematic Design for Emergence in Cellular Nonlinear Networks - page 53

So far we were able to show that complexity can be characterized in many
different ways, other than using the four classes proposed by Wolfram. The
previous examples also suggest the introduction of three measurable quantities
( the transient length, the clustering coefficient and the exponent of growth ) that
can give a synthetic description of the dynamic behavior. It turns out that all
“interesting” phenomena, other than “chaotic” (often used for random number
generators [67,72]) are related to the presence of interacting gliders. These gliders
are acting as basic computational units with predictable behavior and therefore
could be organized into hierarchical structures much like simple logic gates are
used to generate higher levels of complex computing machines.
For instance, Fig. 4.4 depicts interaction between gliders emerging from a ran-
dom initial state in a CA from the 1s5 family (ID=179) where two basic logic
functions (XOR and AND) are implemented as an effect of collision between
gliders. More complex functions can be constructed based on such “spatio-
temporal” gates. Note that some gliders (such as the horizontal one in the picture)
act as reflective and diffractive mediums producing “billiard ball” effects [20] to
be further exploited in defining logic functions. By properly selecting the spatial
distribution of gliders in the initial state and a spatio-temporal location of an out-
put, various logic functions can be implemented, using the same cellular medium
(CA cells with ID=179).
Such cellular mediums may be eventually proved to be universal computers,
where the “program” is now encoded in the initial state distribution of gliders, the
Fig. 4.4. Emergence of gliders in CA with ID=179 and their use to compute basic logic
functions. Within this figure, time is on the horizontal axis, while a vertical column at a
specified iteration represent the collection of states for the CA cells