173 research outputs found
Asynchronism Induces Second Order Phase Transitions in Elementary Cellular Automata
Cellular automata are widely used to model natural or artificial systems.
Classically they are run with perfect synchrony, i.e., the local rule is
applied to each cell at each time step. A possible modification of the updating
scheme consists in applying the rule with a fixed probability, called the
synchrony rate. For some particular rules, varying the synchrony rate
continuously produces a qualitative change in the behaviour of the cellular
automaton. We investigate the nature of this change of behaviour using
Monte-Carlo simulations. We show that this phenomenon is a second-order phase
transition, which we characterise more specifically as belonging to the
directed percolation or to the parity conservation universality classes studied
in statistical physics
Experimental study of Elementary Cellular Automata dynamics using the density parameter
International audienceClassifying cellular automata in order to capture the notion of chaos algorithmically is a challenging problem than can be tackled in many ways.We here give a classification based on the computation of a macroscopic parameter, the -spectrum, and show how our classifying scheme can be used to separate the chaotic ECA from the non-chaotic ones
Aesthetics and randomness in cellular automata
International audienceWe propose two images obtained with an asynchronous and a stochastic cellular automaton. Deterministic cellular automata are now well-studied models and even if there is still so much to understand, their main properties are now largely explored. By contrast, the universe of asynchronous and stochastic is mainly a terra incognita. Only a few islands of this vast continent have been discovered so far. The two examples below present space-time diagrams of one-dimensional cellular automata with nearest-neighbour interaction. The cells are arranged in a ring, that is, the right neighbour of the rightmost cell is the leftmost cell, and vice versa; in formal words, indices are taken in Z/nZ, where n is the number of cells. The space-time diagrams are obtained with the FiatLux software. Time goes from bottom to top: the successive states of the system are stacked one on the other
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
Remarks on the cellular automaton global synchronisation problem – deterministic vs. stochastic models
International audienceIn the global synchronisation problem, one is asked to find a cellular automaton which has the property that every initial condition evolves into a homogeneous blinking state. We study this simple inverse problem for the case of one-dimensional systems with periodic boundary conditions. Two paradoxical observations are made: (a) despite the apparent simplicity of finding rules with good statistical results, there exist no perfect deterministic solutions to this problem, (b) if we allow the use of randomness in the local rule, constructing ``perfect" stochastic solutions is easy. For the stochastic case, we give some rules for which the mean time of synchronisation varies quadratically with the number of cells and ask if this result can be improved.To explore more deeply the deterministic rules, we code our problem as a SAT problem and USE SAT solvers to find rules that synchronise a large set of initial conditions (in appendix)
A note on the Density Classification Problem in Two Dimensions
International audienceThe density classification problem is explored experimentally in the case of two-dimensional grids. We compare the performance of deterministic and stochastic CA, as well as interacting particle systems. The question of how to design a rule that would attain an arbitrary precision is examined and we show that it seems more difficult to solve than in the one-dimensional case
Is there something like ''modellability'' ? - Reflections on the robustness of discrete models of complex systems
International audienceExtended abstract of the talk given in Universidad de Concepcion, Chile, Octobre 21st., 2013. Invitation by Pr. Julio Aracen
Does Life resist asynchrony ?
We study Conway's Game of Life with an asynchronous updating
Self-stabilisation of cellular automata on tilings
Given a finite set of local constraints, we seek a cellular automaton (i.e.,
a local and uniform algorithm) that self-stabilises on the configurations that
satisfy these constraints. More precisely, starting from a finite perturbation
of a valid configuration, the cellular automaton must eventually fall back to
the space of valid configurations where it remains still. We allow the cellular
automaton to use extra symbols, but in that case, the extra symbols can also
appear in the initial finite perturbation. For several classes of local
constraints (e.g., -colourings with , and North-East deterministic
constraints), we provide efficient self-stabilising cellular automata with or
without additional symbols that wash out finite perturbations in linear or
quadratic time, but also show that there are examples of local constraints for
which the self-stabilisation problem is inherently hard. We note that the
optimal self-stabilisation speed is the same for all local constraints that are
isomorphic to one another. We also consider probabilistic cellular automata
rules and show that in some cases, the use of randomness simplifies the
problem. In the deterministic case, we show that if finite perturbations are
corrected in linear time, then the cellular automaton self-stabilises even
starting from a random perturbation of a valid configuration, that is, when
errors in the initial configuration occur independently with a sufficiently low
density.Comment: 43 pages, 28 figure
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