元胞自动机与格子气

Continuous cellular automata are rocketing in popularity, yet developing a theoretical understanding of their behaviour remains a challenge. In the case of Lenia, a few fundamental open problems include determining what exactly constitutes…

The minimal number of inputs in the local function of a non-trivial cellular automaton is two. Such a function can be viewed as as a kind of binary operation. If this operation is associative, it forms, together with the set of states, a…

The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approximation works surprisingly well for some cellular automata,…

For many cellular automata, it is possible to express the state of a given cell after $n$ iterations as an explicit function of the initial configuration. We say that for such rules the solution of the initial value problem can be obtained.…

We propose to extend the multiresolution relaxation times lattice Boltzmann schemes with an additional projection step. For the explicit example of the D2Q9 scheme, we define this extended method. We prove that in general the projection…

Cellular automata (CA) are quintessential ALife and ubiquitous in many studies of collective behaviour and emergence, from morphogenesis to social dynamics and even brain modelling. Recently, there has been an increased interest in…

One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…

We investigate Frobenius-driven revivals in prime-modulus Laplacian cellular automata, a phenomenon in which long chaotic transients collapse into exact, multi-tile replicas of an initial seed at algebraically prescribed times $t=p^m$. The…

This paper demonstrates accurate traffic modeling and forecast using stochastic cell-automata (CA) and distributed fiber-optic sensing (DFOS). Traffic congestion is a dominant issue in highways. To reduce congestion, real-time traffic…

We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy…

Cellular automata on the triangular grid are here referred to as Triangular Automata (TA). This paper focuses on the simplest class of TA, called Elementary Triangular Automata (ETA). They are argued to be the two-dimensional counterpart of…

The Lights Out Puzzle represents a cellular automaton based on a grid of squares where clicking a square changes its state and the states of surrounding squares. A "quiet pattern" is a way to click such that in the end, no change is…

Self-replication is central to all life, and yet how it dynamically emerges in physical, non-equilibrium systems remains poorly understood. Von Neumann's pioneering work in the 1940s and subsequent developments suggest a natural hypothesis:…

We present a strong theoretical foundation that frames a well-defined family of outer-totalistic network automaton models as a topological generalisation of binary outer-totalistic cellular automata, of which the Game of Life is one notable…

Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their…

Lenia is a continuous extension of Conway's Game of Life that exhibits rich pattern formations including self-propelling structures called gliders. In this paper, we focus on Asymptotic Lenia, a variant formulated as partial differential…

We offer detailed proofs of some properties of the Rule 60 cellular automaton on a ring with a Mersenne number circumference. We then use these properties to define a propagator, and demonstrate its use to construct all the ground state…

Autonomous vehicles are essential to future transportation systems, potentially reducing traffic congestion. This study examines the impact of different vehicle control strategies on traffic flow through simulations. We propose a novel…

This paper explores the use of 2D cellular automata (CA) to generate 3D terrains through a simple additive approach. Experimenting with multiple CA transition rules produced aesthetically interesting, navigable landscapes, suggesting…

Elementary Cellular Automata (ECAs) exhibit diverse behaviours often categorized by Wolfram's qualitative classification. To provide a quantitative basis for understanding these behaviours, we investigate the global dynamics of such…