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Based on computer simulations Wolfram presented in several papers conjectured classifications of cellular automata into 4 types. He distinguishes the 4 classes of cellular automata by the evolution of the pattern generated by applying a…
We study one dimensional binary Probabilistic Cellular Automaton (PCA) that interpolate between Wolfram's classical rules 23, 77, 178 and 232. These rules are the only ones that satisfy two criteria: (i) in the case of a majority in the…
We define a cellular automaton where a resting cell excites if number of its excited neighbours belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbours in the cell's…
We investigate the stability of general-relativistic boson stars by classifying singularities of differential mappings and compare it with the results of perturbation theory. Depending on the particle number, the star has the following…
We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations…
We study two-dimensional cellular automata, each cell takes three states: resting, excited and refractory. A resting cell excites if number of excited neighbours lies in a certain interval (excitation interval). An excited cell become…
Three reasonable hypotheses lead to the thesis that physical phenomena can be described and simulated with cellular automata. In this work, we attempt to describe the motion of a particle upon which a constant force is applied, with a…
A simple model of particle creation and annihilation in an isolated assembly of particles with conserved energy and fixed volume, the Cell Model, is formulated. With increasing time, particle number distribution, obtained by averaging over…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
We consider the problem of metastability for stochastic reversible dynamics with exponentially small transition probabilities. We generalize previous results in several directions. We give an estimate of the spectral gap of the transition…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
Microbiological systems evolve to fulfill their tasks with maximal efficiency. The immune system is a remarkable example, where self-non self distinction is accomplished by means of molecular interaction between self proteins and antigens,…
We consider the problem of metastability in a probabilistic cellular automaton (PCA) with a parallel updating rule which is reversible with respect to a Gibbs measure. The dynamical rules contain two parameters $\beta$ and $h$ which…
We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single…
Landslide inventories show that the statistical distribution of the area of recorded events is well described by a power law over a range of decades. To understand these distributions, we consider a cellular automaton to model a time and…
A variant of Kauffman's model of cellular metabolism is presented. It is a randomly generated network of boolean gates, identical to Kauffman's except for a small bias in favor of boolean gates that depend on at most one input. The bias is…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…