Related papers: k-Mixing Properties of Multidimensional Cellular A…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
A neighborhood for d-dimensional cellular automata is introduced that spans the range from von Neumann to Moore neighborhood using a parameter which represents the dimension of hypercubes connecting neighboring cells. The neighborhood is…
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 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…
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…
Cellular automata can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schr\"odinger equation together with its conservation laws. Surprisingly, a whole class of…
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,…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
A general family of $D$-dimensional, $K$-state cellular automata is proposed where the update rule is sequentially applied in each dimension. This includes the Biham--Middleton--Levine traffic model, which is a 2D cellular automaton with 3…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
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…
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…
We define and explore in simulation several rules for the local evolution of generative rules for 1D and 2D cellular automata. Our implementation uses strategies from conceptual blending. We discuss potential applications to modelling…
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…
In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
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…
Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by…
Fekete's lemma is a well known combinatorial result on number sequences: we extend it to functions defined on $d$-tuples of integers. As an application of the new variant, we show that nonsurjective $d$-dimensional cellular automata are…