Related papers: Wave propagation in filamental cellular automata
We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
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…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
Filamentous cyanobacteria can show fascinating examples of nonequilibrium self-organization, which however are not well-understood from a physical perspective. We investigate the motility and collective organization of colonies of these…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
We created two dimensional hexagonal cellular automata to obtain complexity. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
Sustained rhythmic oscillations, pulsing dynamics, emerge spontaneously when the local connection scheme is randomised in 3-value cellular automata that feature"glider" dynamics. Time-plots of pulsing measures maintain a distinct waveform…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
We show that the correlation and entanglement dynamics of spin systems can be understood in terms of propagation of spin waves. This gives a simple, physical explanation of the behaviour seen in a number of recent works, in which a…
Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature…
We propose a probabilistic cellular automata model for the spread of innovations, rumors, news, etc. in a social system. The local rule used in the model is outertotalistic, and the range of interaction can vary. When the range R of the…