Related papers: An Invitation to Number-Conserving Cellular Automa…
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…
A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…
Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular…
New Cellular Automata associated with the Schroedinger discrete spectral problem are derived. These Cellular Automata possess an infinite (countable) set of constants of motion.
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
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…
In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…
This paper presents a rotation-invariant embedded platform for simulating (neural) cellular automata (NCA) in modular robotic systems. Inspired by previous work on physical NCA, we introduce key innovations that overcome limitations in…
We present some computer simulations run on a stochastic CA (cellular automaton). The CA simulates a gas of particles which are in a channel, the interval $[1,L]$ in $\mathbb Z$, but also in "reservoirs" $\mathcal R_1$ and $\mathcal R_2$.…
Several cellular automata (CA) models have been developed to simulate self-organization of multiple levels of structures. However, they do not obey microscopic reversibility and conservation laws. In this paper, we describe the construction…
Cell biomechanics involve a great number of complex phenomena that are fundamental to the evolution of life itself and other associated processes, ranging from the very early stages of embryo-genesis to the maintenance of damaged structures…
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…
Biological systems exhibit remarkable morphogenetic plasticity, where a single genome can encode various specialized cellular structures triggered by local chemical signals. In the domain of Deep Learning, Differentiable Neural Cellular…
We study the dynamics of (synchronous) one-dimensional cellular automata with cyclical boundary conditions that evolve according to the majority rule with radius $ r $. We introduce a notion that we term cell stability with which we express…
This paper describes a new concept of cellular automaton (CA). XCA consists of a set of arcs (edges) that correspond to cells in CA. At a particular time, the arcs are connected to a directed graph. With each time step, the arcs exchange…
This paper presents an application of the Infinite Unit Axiom, introduced by Yaroslav Sergeyev, (see [11] - [14]) to the development of one-dimensional cellular automata. This application allows the establishment of a new and more precise…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
A stochastic cellular automata (CA) model for pedestrian dynamics is presented. Our goal is to simulate different types of pedestrian movement, from regular to panic. But here we emphasize regular situations which imply that pedestrians…
We propose Neural Cellular Automata (NCA) to simulate the microstructure development during the solidification process in metals. Based on convolutional neural networks, NCA can learn essential solidification features, such as preferred…
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…