Related papers: A compact topology for sand automata
We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\"odinger…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
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…
Eilenberg's holonomy decomposition is useful to ascertain the structural properties of automata. Using this method, Egri-Nagy and Nehaniv characterized the absence of certain types of cycles in automata. In the direction of studying the…
We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional…
We consider asynchronous networks of identical finite (independent of network's size or topology) automata. Our automata drive any network from any initial configuration of states, to a coherent one in which it can carry efficiently any…
The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally…
Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions…
We establish several extensions of the well-known Garden of Eden theorem for non-uniform cellular automata over the full shifts and over amenable group universes. In particular, our results describe quantitatively the relations between the…
We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore not be tame and the topological sequence entropy is strictly…
Gravitational clustering of a random distribution of point masses is dominated by the effective short-range interactions due to large-scale isotropy. We introduce a one-dimensional cellular automaton to reproduce this effect in the most…
Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into…
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…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…