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Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
We investigate numerically the critical behaviour of a one-dimensional non-attractive lattice gas model that is the continuous-time version of the Domany-Kinzel cellular automaton in one of its parameter subspaces. The model shows a phase…
We study transport properties in a slowly driven diffusive system where the transport is externally controlled by a parameter $p$. Three types of behavior are found: For $p<p'$ the system is not conducting at all. For intermediate $p$ a…
Phase transitions and critical behavior of driven systems are reviewed. Models exhibiting phase transitions, spontaneous symmetry breaking, phase separation and coarsening processes in d=1 dimension are discussed.
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…
We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
In this work a three-states cellular automaton proposed to describe part of a biological immune system is revisited. We obtain the dynamic critical exponent $z$ of the model by means of a recent technique that mixes different initial…
We study the effect of mixing two rules on the dynamics of one-dimensional cellular automata by large scale numerical simulations. We calculate the decay of the magnetization for the Domany-Kinzel automaton (XOR/AND mixing) to its…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step.…
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…
Starting from integrable cellular automata we present a novel form of Painlev\'e equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The…
In line with the stability theory of continuous dynamical systems, Lyapunov exponents of cellular automata (CAs) have been conceived two decades ago to quantify to what extent their dynamics changes following a perturbation of their initial…
We show that non-locality in the conservation of both the order parameter and a noncritical density (model D dynamics) leads to new fixed points for critical dynamics. Depending upon the parameters characterizing the non-locality in the two…
Sand pile formation is often used to describe stratified chaos in dynamic systems due to self-emergent and scale invariant behaviour. Cellular automata (Bak-Tang-Wiesenfeld model) are often used to describe chaotic behaviour, as simulating…
This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability,…