Related papers: Hard Asymptotic Sets for One-Dimensional Cellular …
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…
The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic "rock-paper-scissors" prey-predator relationship. Starting from a random configuration, similar states gather in increasingly…
We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically…
Let $h,k \ge 2$ be integers. We say a set $A$ of positive integers is an asymptotic basis of order $k$ if every large enough positive integer can be represented as the sum of $k$ terms from $A$. A set of positive integers $A$ is called…
Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random…
Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect…
This investigation studies the ergodic properties of reversible linear cellular automata over $\mathbb{Z}_m$ for $m \in \mathbb{N}$. We show that a reversible linear cellular automaton is either a Bernoulli automorphism or non-ergodic. This…
We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time…
Building on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties [10], we introduce a notion of cellular automata over schemes which generalize affine algebraic cellular automata in [7]. We extend known results to…
We develop a rather elaborate computer program to investigate the jointly periodic points of one-dimensional cellular automata. The experimental results and mathematical context lead to questions, conjectures and a contextual theorem.
The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between…
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…
In this paper, we construct a weakly universal cellular automaton in the heptagrid, the tessellation $\{7,3\}$ which is not rotation invariant but which is truly planar. This result, under these conditions, cannot be improved for the…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
We study groups of reversible cellular automata, or CA groups, on groups. More generally, we consider automorphism groups of subshifts of finite type on groups. It is known that word problems of CA groups on virtually nilpotent groups are…
Fuzzy cellular automaton is a dynamical system with a continuous state value embedding a cellular automaton with a discrete state value. We investigate a fuzzy cellular automaton obtained from an elementary cellular automaton of rule number…
Most slowly synchronizing automata over binary alphabets are circular, i.e., containing a letter permuting the states in a single cycle, and their set of synchronizing words has maximal state complexity, which also implies complete…
In this paper, we prove that there is a strongly universal cellular automaton on the heptagrid with seven states which is rotation invariant. This improves a previous paper of the author where the automaton required ten states.