Emergence, Locating and Measuring It - Systematic Design for Emergence in Cellular Nonlinear Networks - page 47

visual observation is the main instrument based on which Wolfram recently
proposed his “new kind of science” [17,55]. Since the visual observation is done
by humans, besides a certain subjectivity, if one would like to analyze a large
population of cells in terms of the emergent behaviors, such a visual detection of
the “surprise” effect would be boring or even impossible in a reasonable interval
of time. Another questionable issue is the classification of global behaviors. So far
the taxonomy proposed by Wolfram [56] with four main classes, is quite largely
accepted although several others were recently proposed [57]. But one issue ob-
served in many works is that for some special cases it would be quite difficult to
choose among classes, therefore the boundaries between classes are rather fuzzy
than crisp [58].
The aim of the research described herein is to introduce and exemplify a set of
tools to evaluate numerically the global behavior of a cellular system. Since these
tools are computer programs, they eliminate the human factor in observing emer-
gence. The result is that an exhaustive analysis of the relationship between local
cells and global behaviors can be done automatically, considering very large popu-
lations of cells. Moreover, the tools introduced herein allow one to develop design
for emergence programs where a desired global behavior can be now quantified
numerically as an objective function of an optimization algorithm.
4.2 Visual Interpretation of Emergent
Phenomena - Classes of Behaviors
According to Wolfram [56] behaviors in a cellular automata (starting from a ran-
dom initial state) shall fall into one of the following four classes:
x Class I - Dull behavior, the cellular automata converges towards a pattern
where all states of the cell are the same. This class may also correspond to the
“passivity” concept introduced in [7,8].
x Class II - Simple dynamic behavior, the cellular automata converges to a finite
(alternating) number of states (fixed points with states that may differ from one
cell to another or low periodicity, as spoken in nonlinear dynamics parlance).
x Class III - Is defined by Wolfram as “random” behaviors (corresponding to
chaotic or aperiodic regimes in nonlinear dynamics parlance).
x Class IV - This is the most interesting according to Wolfram and it is vaguely
defined as a “mixture of order and randomness” with “interacting structures”.
One interesting idea comes from this definition, namely the “interacting struc-
tures” also called gliders in a simpler parlance. Indeed it turned out that gliders
are crucial for demonstrating universal computation and emergence in cellular
systems and therefore we would like to insist more on them.