Related papers: Four state deterministic cellular automaton rule e…
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…
In this work, we formulate a theoretical model based on a cellular automaton (CA) to study thermal transport in low-dimensional nanostructures across ballistic, diffusive, and transition regimes. Unlike computationally intensive methods…
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…
This paper studies the number conservation property of 1-dimensional non-uniform cellular automata (CAs). In a non-uniform cellular automaton (CA), different cells may follow different rules. The present work considers that the cells follow…
This article presents a new characterization of controllability and regional controllability of Deterministic Cellular Automata (CA for short). It focuses on analyzing these problems within the framework of control theory, which have been…
A cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement…
We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature…
We study one-dimensional reversible and number-conserving cellular automata (RNCCA) that have both properties of reversibility and number-conservation. In the case of 2-neighbor RNCCA, Garc\'ia-Ramos proved that every RNCCA shows trivial…
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…
We present evidence that operation of QCA (Quantum Cellular Automaton) cells with four dots is possible with an occupancy of 4N+2 electrons per cell (N being an integer). We show that interaction between cells can be described in terms of a…
The purpose of the present study is to search one-dimensional Cellular Automata (CA) rules which will solve the density classification task (DCT) perfectly. The mathematical analysis of number conserving functions over binary strings of…
Various non-classical approaches of distributed information processing, such as neural networks, computation with Ising models, reservoir computing, vector symbolic architectures, and others, employ the principle of collective-state…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations…
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…
A new paradigm for the unification of physics is described. It is called Cellular Automata (CA) theory, which is the most massively parallel computer model currently known to science. We maintain that at the tiniest distance and time scales…
One of the most important problems in contemporary science, and especially in biology, is to reveal mechanisms of pattern formation. On the level of biological tissues, patterns form due to interactions between cells. These interactions can…
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…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…