Related papers: A Particular Universal Cellular Automaton
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
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…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the…
Automata-based modeling languages, like Component Interaction Automata, offer an attractive means to capture and analyze the behavioral aspects of interacting components. At the center of these modeling languages we find finite state…
I describe a quantum cellular automaton capable of performing universal quantum computation. The automaton has an elementary transition function that acts on Margolus cells of $2\times 2$ qubits, and both the ``quantum input'' and the…
We discuss the role of classical control in the context of reversible quantum cellular automata. Employing the structure theorem for quantum cellular automata, we give a general construction scheme to turn an arbitrary cellular automaton…
We present evidence that operation of QCA (Quantum Cellular Automaton) cells with four dots is possible with an occupancy of 4N+2 electrons per cell (N being an integer). We show that interaction between cells can be described in terms of a…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
There are few known universality classes of absorbing phase transitions in one dimension and most models fall in the well-known directed percolation (DP) class. Synchronization is a transition to an absorbing state and this transition is…
We construct a time-optimal quasi-solution of the firing mob synchronisation problem over finite, connected, and undirected multigraphs whose maximum degrees are uniformly bounded by a constant. It is only a quasi-solution because its…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of…
Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in…
Clifford quantum cellular automata (CQCAs) are a special kind of quantum cellular automata (QCAs) that incorporate Clifford group operations for the time evolution. Despite being classically simulable, they can be used as basic building…
Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or…
An additive cellular automaton is a linear map on the set of infinite multidimensional arrays of elements in a finite cyclic group $\mathbb{Z}/m\mathbb{Z}$. In this paper, we consider simplices appearing in the orbits generated from…
We investigate how increasing the dimension of the array can help to draw signals on cellular automata.We show the existence of a gap of constructible signals in any dimension. We exhibit two cellular automata in dimension 2 to show that…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…