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when the state of a cell is not influenced by the environment). Furthermore,
ordered patterns emerge, like in dissipative systems [11], when the external per-
turbation is higher than a critical value and they are present for a specific per-
turbation strength range.
On this basis, the paper argues that similar sort of macro-level behaviors
are likely to emerge as soon as multiagent systems (or likes)will start popu-
lating the Internet and our physical spaces, both characterized by intrinsic and
unpredictable dynamics. Such behaviors are likely to dramatically influence the
overall behavior of our networks at a very large scale. This may require new mod-
els, methodologies, and tools, explicitly taking into account the environmental
dynamics, and exploiting it during software design and development either de-
fensively, to control its effects on the system, or constructively, as an additional
design dimension.
This paper is organized as follows. Sect. 2 defines DCA as CA characterized
by asynchronous dynamics and openness. In Sect. 3 we describe experiments and
we discuss the results obtained. In Sect. 4 the relation between DCA and dissi-
pative systems is further investigated, by showing the typical system behavior
as a function of the external perturbation. We conclude with Sect. 5 outlining
potential applications and future work.
2 Dissipative Cellular Automata
In this section we first briefly recall the definition of Cellular Automata (CA)
and introduce the terminology that will be used in the following. Then, we de-
fine Dissipative Cellular Automata (DCA)as CA characterized by
asynchronous
dynamics and
openness
.
A CA is defined by a quadruple
A
=(
S, d, V, f
), where
S
is the finite set
of possible states a cell can assume,
d
is the dimension of the automaton,
V
is
the neighborhood structure, and
f
is the local transition rule. In this work we
assume what follows:
- The automaton structure is a 2-dimensional discrete grid closed to a 2-
dimensional torus (namely,
N × N
square grids with wraparound borders).
- The neighborhood structure is regular and isotropic, i.e.,
V
has the same
definition for every cell.
-
f
is the same for each cell (uniform CA).
The quadruple
A
specifies the static characteristics of an automaton. The com-
plete description of a CA requires the definition of its dynamics, i.e., of the
dynamics ruling the update of the state of CA cells. In general, the dynamics of
a CA assumes a discrete time. The usual definition of CA is with synchronous
dynamics: cells update their state in parallel at each time step.
Synchronous CA of this kind have been deeply studied [19,1] and have
also an interesting biological/systemic interpretation: cells can be interpreted
as alive/dead, or system elements active/inactive depending on their state.
