Related papers: An Expressive Coalgebraic Modal Logic for Cellular…
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…
We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…
We introduce the Concurrent Modular Agent (CMA), a framework that orchestrates multiple Large-Language-Model (LLM)-based modules that operate fully asynchronously yet maintain a coherent and fault-tolerant behavioral loop. This framework…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the…
A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations).…
This contribution belongs to a combinatorial approach to hyperbolic geometry and it is aimed at possible applications to computer simulations. It is based on the splitting method which was introduced by the author and which is reminded in…
The prediction of the behavior of the disease, the level of affectation in a population and the ways to control it are the most important aspects studied by epidemiology using tools such as historical data and mathematical models. So, our…
Cellular automata, CA for short are continuous maps defined on the set of configurations over a finite alphabet A that commutes with the shift. They are characterized by the existence of local function which determine by local behavior the…
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…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
Quantifying the outcomes of cells collisions is a crucial step in building the foundations of a kinetic theory of living matter. Here, we develop a mechanical theory of such collisions by first representing individual cells as extended…
This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
We show that a behaviour analogous to degenerate hyperbolicity can occur in nearest-neighbour cellular automata (CA) with three states. We construct a 3-state rule by "lifting" elementary CA rule 140. Such "lifted" rule is equivalent to…
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…
For an arbitrary group $G$ and arbitrary set $A$, we define a monoid structure on the set of all uniformly continuous functions $A^G\to A$ and then we show that it is naturally isomorphic to the monoid of cellular automata $\mathrm{CA}(G,…
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their…
We define a cellular automaton where a resting cell excites if number of its excited neighbours belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbours in the cell's…
In this paper, we perform a theoretical analysis of the sequential convergence of elementary cellular automata that have at least one fixed point. Our aim is to establish which elementary rules always reach fixed points under sequential…