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strictly local rules, tend to reach a local equilibrium (or a strictly local dynamics),
which produce a global uniform equilibrium of the whole system.
When the system is kept in a substantial out-of-equilibrium situation, the
locally reached equilibrium situations are continuously perturbed, resulting in
continuous attempt to locally reestablish equilibrium. This typically ends up
with cell groups having found new equilibrium states more robust with regard
to the perturbation (or compatible with it). Such stable local patterns start
soon dominating and influencing the surrounding, in a sort of positive feedback,
until a globally coordinated (i.e., with large-scale spatial patterns)and stable
situation emerges.
When the degree of perturbation is high enough to avoid local stable situa-
tions to persist for enough time, they can no longer influence the whole systems,
and the situation becomes turbulent.
5 Conclusion and Future Work
This paper has reported the outcomes of a set of experiments performed on a
new class of cellular automata, DCA, which are open to the environment and
can be perturbed by its dynamics. These experiments have shown that the per-
turbation makes large-scale symmetry breaking spatial structures, not observed
under closed regime, emerge. By introducing a measure of the randomness of
DCA states we have shown that structures emerge when the external perturba-
tion is higher than a critical value and below the turbulence limit.
The experiments reported in this paper are indeed preliminary, and further
work is in progress:
-
we are currently exploring different measures for evaluating the emergence of
large-scale patterns. For example, we may consider techniques analogous to
the ones presented in [4,3,5], where structure is measured by evaluating the
complexity of the probabilistic automaton reconstructed from the data series
representing the CA evolution. Other possibilities rely on the application of
techniques derived from image analysis (for example, we may use spatial
correlation measures);
-
we are extending our DCA simulation framework so as to study the behavior
of network structures other than the regular ones of DCA, such as small-
world graphs [18] and boolean networks [9], as well as networks with mobile
nodes;
-
we intend to perform further experiments to evaluate the behavior of DCA
under different perturbation regimes and to experiment with more complex
DCA, i.e., DCA with large set of states and/or with non-uniform transition
functions [17,16].
The results presented in this paper promise to have several potential implica-
tions in the area of distributed computing. In fact, DCA exhibit characteristics
(i.e., autonomy of components, locality in interactions, openness to the envi-
ronment)that are typical of modern distributed computing environments, e.g.,
sensor networks and multi-agent systems.
