1,161 research outputs found
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
An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata
Cellular Automata (CA) are a class of discrete dynamical systems that have
been widely used to model complex systems in which the dynamics is specified at
local cell-scale. Classically, CA are run on a regular lattice and with perfect
synchronicity. However, these two assumptions have little chance to truthfully
represent what happens at the microscopic scale for physical, biological or
social systems. One may thus wonder whether CA do keep their behavior when
submitted to small perturbations of synchronicity.
This work focuses on the study of one-dimensional (1D) asynchronous CA with
two states and nearest-neighbors. We define what we mean by ``the behavior of
CA is robust to asynchronism'' using a statistical approach with macroscopic
parameters. and we present an experimental protocol aimed at finding which are
the robust 1D elementary CA. To conclude, we examine how the results exposed
can be used as a guideline for the research of suitable models according to
robustness criteria.Comment: Version : Feb 13th, 2004, submitted to Complex System
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
Boolean Delay Equations: A simple way of looking at complex systems
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with
Boolean-valued variables that evolve in continuous time. Systems of BDEs can be
classified into conservative or dissipative, in a manner that parallels the
classification of ordinary or partial differential equations. Solutions to
certain conservative BDEs exhibit growth of complexity in time. They represent
therewith metaphors for biological evolution or human history. Dissipative BDEs
are structurally stable and exhibit multiple equilibria and limit cycles, as
well as more complex, fractal solution sets, such as Devil's staircases and
``fractal sunbursts``. All known solutions of dissipative BDEs have stationary
variance. BDE systems of this type, both free and forced, have been used as
highly idealized models of climate change on interannual, interdecadal and
paleoclimatic time scales. BDEs are also being used as flexible, highly
efficient models of colliding cascades in earthquake modeling and prediction,
as well as in genetics. In this paper we review the theory of systems of BDEs
and illustrate their applications to climatic and solid earth problems. The
former have used small systems of BDEs, while the latter have used large
networks of BDEs. We moreover introduce BDEs with an infinite number of
variables distributed in space (``partial BDEs``) and discuss connections with
other types of dynamical systems, including cellular automata and Boolean
networks. This research-and-review paper concludes with a set of open
questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular
the discussion on partial BDEs is updated and enlarge
Identification of cellular automata: theoretical remarks
Land use evolution during forty years in a large set of European cities is analysed by means of a cellular automaton. In one hand (the operational level), the use of this modelling tool allows: a: to study the transition rules in land use and the proximity effects on these rules; b: to compare the different case -studies, otherwise very difficult to be confronted; c: to define scenarios of evolution, on the bases of the past trends. On the other hand (methodological level), availability of a large data-base (significant time series for a set of comparable cases) allows: a: to manage, in a scientific way, the problem of calibration and validation of a cellular automaton (a crucial problem - we have to blame - usually neglected in territorial applications); b: to verify, empirically, potentialities and limits of cellular automata, compared to other models for the analysis of spatial dynamics.
Surface Structure and Catalytic Oxidation Oscillations
A cellular automaton model is used to describe the dynamics of the catalytic
oxidation of on a surface. The cellular automaton rules account
for the structural phase transformations of the substrate, the reaction
kinetics of the adsorbed phase and diffusion of adsorbed species. The model is
used to explore the spatial structure that underlies the global oscillations
observed in some parameter regimes. The spatiotemporal dynamics varies
significantly within the oscillatory regime and depends on the harmonic or
relaxational character of the global oscillations. Diffusion of adsorbed
plays an important role in the synchronization of the patterns on the substrate
and this effect is also studied.Comment: Latex file with six postscript figures. To appear in Physica
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