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This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…
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…
We present a 2-dimensional cellular automaton model for the simulation of pedestrian dynamics. The model is extremely efficient and allows simulations of large crowds faster than real time since it includes only nearest-neighbour…
Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or…
The cellular automaton (CA) pulsing model (arXiv:1806.06416) described the surprising phenomenon of spontaneous, sustained and robust rhythmic oscillations, pulsing dynamics, when random wiring is applied to a 2D `glider' rule running in a…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for \cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to…
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…
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 study the dynamics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics, corresponding to a bulk deterministic and reversible discrete…
Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under…
This is a study of the one-dimensional elementary cellular automaton rule 54 in the new formalism of "flexible time". We derive algebraic expressions for groups of several cells and their evolution in time. With them we can describe the…
Cellular automata can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schr\"odinger equation together with its conservation laws. Surprisingly, a whole class of…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…