Applications of Emergent Phenomena - Systematic Design for Emergence in Cellular Nonlinear Networks - page 129

8

Applications of Emergent Phenomena

8.1 Introduction

Cellular automata were long recognized as having a great potential for applications,
particularly when one have to deal with multi-dimensional signal processing or

modeling. One of the main obstacle was to design CAs, i.e. to select among

many possible cells the ones having a desired behavior. Usually such cells were
randomly selected and the corresponding CA simulated. Then one would associate
certain uses to that particular CA. Not surprisingly, one of the first application of
CA is the random number generator, a behavior which can be characterized, in the
light of the measures defined in the previous chapters, as a behavior with a large
exponent of growth and a clustering coefficient around 0.5. As seen from our
investigations over large families of semi-totalistic cells, there are many CAs with
the above characteristics. Therefore a random selection of CA cells will likely
provide a good number generator.
Other interesting automata are those producing gliders. The famous example of
the Game of Life was found by an educated guess in defining the CA rule heuris-
tically as a simple model of a real life system. Another, more recent example, is
the ID = 110 CA (in our terminology a 1a3 CA) of Wolfram, proved to be the
simplest CA capable of universal computation [17]. It is widely recognized that
finding such CAs by simply picking cells at random is very difficult since it ap-
pears that interesting emergent behaviors are rather sparse within the entire space
of cells. Though, the order introduced by our measures allows identifying similar
behaviors with much ease. For instance, estimating the uncertainty profile as
shown in Chap. 7, for the ID = 110 (Wolfram's universal computation) gives
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u u . A simple inspection of the uncertainty profiles
for all IDs within the 1a3 family gives the following IDs with the same profile or
its mirrored version (with respect to the center element): ID = 137, ID = 206 (the
same profile) and ID = 124, ID = 193 and ID = 220 (mirrored profile). Simulation
of ID = 137, 124 and 193 gives the same behavior as in the case of ID = 110 and
these four cells were recently reported as being similar using a different approach
[76]. The presence of another two (ID = 206 and ID = 220) reveals two aspects:
(a) they may be worth investigated further although visually they appear as having

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a different behavior. Indeed the patterns are apparently not so complex but gliders-

like interaction is present in the form of collision between central and laterally