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A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations).…
A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.
We propose an arbitrarily high-order accurate, fully well-balanced numerical method for the one-dimensional blood flow model. The developed method employs a continuous solution representation, combining conservative and primitive…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
We use analytical methods to investigate cellular automata for traffic flow. Two different mean-field approaches are presented, which we call site-oriented and car-oriented, respectively. The car-oriented mean-field theory yields the exact…
We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…
In this paper computer simulation results of higher order density correlation for cellular automaton models of traffic flow are presented. The examinations show the jamming transition as a function of both the density and the magnitude of…
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…
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…
This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…
We construct a two dimensional Cellular Automata based model for the description of pedestrian dynamics. Wide range of complicated pattern formation phenomena in pedestrian dynamics are described in the model, e.g. lane formation, jams in a…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
We present Mass-Conserving Evolution (MaCE), a general method for implementing mass conservation in Cellular Automata (CA). MaCE is a simple evolution rule that can be easily 'attached' to existing CAs to make them mass-conserving, which…
Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in…
Central to the artificial life endeavour is the creation of artificial systems spontaneously generating properties found in the living world such as autopoiesis, self-replication, evolution and open-endedness. While numerous models and…
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…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
We develop a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment (i.e. allowing the momentum of one fluid to be a linear combination of the velocities of all fluids). Maximum use is made of…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…