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The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore…
In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the…
We Propose A Novel Automaton Model which uses Arithmetic Operations as the Evolving Rules, each cell has the states of the Natural Numbers k = (N), a radius of r = 1/2 and operates on an arbitrary input size. The Automaton reads an…
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…
A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their…
We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
We study two common types of time-noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions. We first construct the stationary states using the…
We report surprisingly regular behaviors observed for a class 4 cellular automaton, the totalistic rule 20: starting from disordered initial configurations the automaton produces patterns which are periodic not only in time but also in…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
Biodiversity conservation becoming increasingly urgent. It is important to find mechanisms of competitive coexistence of species with different fitness in especially difficult circumstances - on one limiting resource, in isolated stable…
We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
We propose that the behaviour of non-linear media can be controlled automatically through coevolutionary systems. By extension, forms of unconventional computing, i.e., massively parallel non-linear computers, can be realised by such an…
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 propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…
Conway's Game of Life is the best-known cellular automaton. It is a classic model of emergence and self-organization, it is Turing-complete, and it can simulate a universal constructor. The Game of Life belongs to the set of semi-totalistic…
A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the…