2,291 research outputs found
On the decomposition of stochastic cellular automata
In this paper we present two interesting properties of stochastic cellular
automata that can be helpful in analyzing the dynamical behavior of such
automata. The first property allows for calculating cell-wise probability
distributions over the state set of a stochastic cellular automaton, i.e.
images that show the average state of each cell during the evolution of the
stochastic cellular automaton. The second property shows that stochastic
cellular automata are equivalent to so-called stochastic mixtures of
deterministic cellular automata. Based on this property, any stochastic
cellular automaton can be decomposed into a set of deterministic cellular
automata, each of which contributes to the behavior of the stochastic cellular
automaton.Comment: Submitted to Journal of Computation Science, Special Issue on
Cellular Automata Application
Response Curves and Preimage Sequences of Two-Dimensional Cellular Automata
We consider the problem of finding response curves for a class of binary
two-dimensional cellular automata with -shaped neighbourhood. We show that
the dependence of the density of ones after an arbitrary number of iterations,
on the initial density of ones, can be calculated for a fairly large number of
rules by considering preimage sets. We provide several examples and a summary
of all known results. We consider a special case of initial density equal to
0.5 for other rules and compute explicitly the density of ones after
iterations of the rule. This analysis includes surjective rules, which in the
case of -shaped neighbourhood are all found to be permutive. We conclude
with the observation that all rules for which preimage curves can be computed
explicitly are either finite or asymptotic emulators of identity or shift.Comment: 7 pages, 3 figure
Localization dynamics in a binary two-dimensional cellular automaton: the Diffusion Rule
We study a two-dimensional cellular automaton (CA), called Diffusion Rule
(DR), which exhibits diffusion-like dynamics of propagating patterns. In
computational experiments we discover a wide range of mobile and stationary
localizations (gliders, oscillators, glider guns, puffer trains, etc), analyze
spatio-temporal dynamics of collisions between localizations, and discuss
possible applications in unconventional computing.Comment: Accepted to Journal of Cellular Automat
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
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