5,366 research outputs found
A study of stochastic 2D Minority CA : would wearing stripes be a fatality for snob people ?
Cellular automata are usually associated with synchronous deterministic dynamics, and their asynchronous or stochastic versions have been far less studied although relevant for modeling purposes. The study of their asynchronous dynamics is all the more needed that their asynchronous behaviors are drastically different from their synchronous ones. This paper analyzes the dynamics of a two-dimensional cellular automaton, 2D Minority, under fully asynchronous dynamics, where only one random cell updates at each time step. This cellular automaton is of particular interest in computer science, biology or social science for instance, and already presents a rich variety of behaviors although the apparent simplicity of its transition rule. In particular, it captures some important features, like the emergence of striped patterns, which are common, according to experiments, to other important automata, such as Game of Life. In this paper, we present a mathematical analysis of the first steps and the last steps of the asynchronous dynamics of 2D Minority. Our results are based on the definition of an interaction energy and rely on the analysis of the dynamics of the borders between competing regions. Our results are a first step towards a complete analysis of this stochastic cellular automaton. Many questions remain open: in particular describing mathematically the middle part of the evolution of 2D Minority where many regions compete with each other, or defining similar parameters (energy, borders,...) for other automata (such as Game of Life) that present similarities with 2D Minority in their asynchronous behaviors
Intrinsic Simulations between Stochastic Cellular Automata
The paper proposes a simple formalism for dealing with deterministic,
non-deterministic and stochastic cellular automata in a unifying and composable
manner. Armed with this formalism, we extend the notion of intrinsic simulation
between deterministic cellular automata, to the non-deterministic and
stochastic settings. We then provide explicit tools to prove or disprove the
existence of such a simulation between two stochastic cellular automata, even
though the intrinsic simulation relation is shown to be undecidable in
dimension two and higher. The key result behind this is the caracterization of
equality of stochastic global maps by the existence of a coupling between the
random sources. We then prove that there is a universal non-deterministic
cellular automaton, but no universal stochastic cellular automaton. Yet we
provide stochastic cellular automata achieving optimal partial universality.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models
In recent years, advances in computational power and spatial data analysis
(GIS, remote sensing, etc) have led to an increase in attempts to model the
spread and behvaiour of wildland fires across the landscape. This series of
review papers endeavours to critically and comprehensively review all types of
surface fire spread models developed since 1990. This paper reviews models of a
simulation or mathematical analogue nature. Most simulation models are
implementations of existing empirical or quasi-empirical models and their
primary function is to convert these generally one dimensional models to two
dimensions and then propagate a fire perimeter across a modelled landscape.
Mathematical analogue models are those that are based on some mathematical
conceit (rather than a physical representation of fire spread) that
coincidentally simulates the spread of fire. Other papers in the series review
models of an physical or quasi-physical nature and empirical or quasi-empirical
nature. Many models are extensions or refinements of models developed before
1990. Where this is the case, these models are also discussed but much less
comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the
International Journal of Wildland Fir
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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