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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…
We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an ``average…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system's evolution after deflection…
A number-conserving cellular automaton is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modelization of the physical…
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…
This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
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…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and…
The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular…
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…
In cellular automata models a glider gun is an oscillating pattern of non-quiescent states that periodically emits traveling localizations (gliders). The glider streams can be combined to construct functionally complete systems of logical…
An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule. Each cell updates its current state depending on current states of its immediate neighbours…
This paper introduces a hierarchical cellular automaton (HCA)model for simulation of distributed self-organizing control of traffic signals at intersections in road network. The proposed HCA consists of three hierarchy levels that describe…
We explore the dynamics of a one-dimensional lattice of state machines on two states and two symbols sequentially updated via a process of "reflexive composition." The space of 256 machines exhibits a variety of behavior, including…
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…
In this paper we study updating effects on cellular automata rule space. We consider a subset of 6144 order-3 automata from the space of 262144 bi-dimensional outer-totalistic rules. We compare synchronous to asynchronous and sequential…
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…