Related papers: Enumeration of number-conserving cellular automata…
A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…
This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
We give a necessary and sufficient condition for the existence of an increasing coupling of $N$ ($N \geq 2$) synchronous dynamics on $S^{\mathbb Z^d}$(PCA). Increasing means the coupling preserves stochastic ordering. We first present our…
Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two…
We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs…
We investigate dynamics of the cellular automaton rule 142. This rule possesses additive invariant of the second order, namely it conserves the number of blocks 10. Rule 142 can be alternatively described as an operation on a binary string…
Quantum-dot Cellular Automata (QCA) provides a basis for classical computation without transistors. Many simulations of QCA rely upon the so-called Intercellular Hartree Approximation (ICHA), which neglects the possibility of entanglement…
Quantum cellular automata are important tools in understanding quantum dynamics, thanks to their simple and effective list of rules. Here we investigate explicitly how coherence is built and lost in the evolution of one-dimensional automata…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…
The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
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…
In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
An interleaving sequence is obtained by combining or intertwining elements from two or more sequences. On the other hand, cellular automata are known to be generators for keystream sequences. In this paper we present two families of…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
Elementary cellular automata (ECA) present iconic examples of complex systems. Though described only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
Given a (finite) string of zeros and ones, we report a way to determine if the number of ones is less than, greater than, or equal to a prescribed number by applying two sets of cellular automaton rules in succession. Thus, we solve the…