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Emergence of Macro Spatial Structures in
Dissipative Cellular Automata
Andrea Roli
1
and Franco Zambonelli
2
1
DEIS
Universita degli Studi di Bologna
aroli@deis.unibo.it
2
DISMI
Universita di Modena e Reggio Emilia
franco.zambonelli@unimo.it
Abstract.
Thispaperdescribesthepeculiarbehaviorobservedinaclass
of cellular automata that we have defined as
dissipative
, i.e., cellular au-
tomata that are
open
and makes it possible for the environment to in-
fluence their evolution. Peculiar in the dynamic evolution of this class
of cellular automata is that stable macro-level spatial structures emerge
from local interactions among cells, a behavior that does not emerge
when the cellular automaton is
closed
, i.e., when the state of a cell is not
influenced by the external world. Moreover, we observed that Dissipative
Cellular Automata (DCA) exhibit a behavior very similar to that of dis-
sipative structures, as macro-level spatial structures emerge as soon as
the external perturbation exceeds a threshold value and it stays below
the “turbulence” limit. Finally, we discuss possible relations of the per-
formed experiments with the area of open distributed computing, and in
particular of agent-based distributed computing.
1 Introduction
In this paper, we present and discuss a set of experiments that we have per-
formed on a new class of cellular automata that we have defined as
Dissipative
Cellular Automata
(DCA). DCA differ from “traditional” cellular automata in
two characteristics: while “traditional” cellular automata are composed of cells
that interact with each other in a synchronous way and that are influenced in
their evolution only by the internal state of the automata themselves, dissipative
ones are
asynchronous
and
open
. One the one hand, cells update their status
independently of each other, in an “autonomous” way. On the other hand, the
automata live dipped in an environment that can directly influence the internal
behavior of the automata, as in open systems.
The reported experiments show that DCA exhibit peculiar interesting be-
haviors. In particular, during the evolution of the DCA, and despite the out-of-
equilibrium situation induced by the external environment, stable macro-level
spatial structures emerge from local interactions among cells, a behavior that
does not emerge when the cellular automaton is synchronous and closed (i.e.,
