Related papers: One Dimensional $n$ary Density Classification Usin…
A cellular automaton with $n$ states may be used for construction of reversible second-order cellular automaton with $n^2$ states. Reversible cellular automata with hidden parameters discussed in this paper are generalization of such…
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…
There exists algorithms to detect reversibility of cellular automaton (CA) for both finite and infinite lattices taking quadratic time. But, can we identify a $d$-state CA rule in constant time that is always reversible for every lattice…
In this paper, we analyze the algebraic structure of some null boundary as well as some periodic boundary 2-D Cellular Automata (CA) rules by introducing a new matrix multiplication operation using only AND, OR instead of most commonly used…
In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…
The objective is to find a Cellular Automata rule that can form a 2D point pattern with a maximum number of points (1-cells). Points are not allowed to touch each other, they have to be separated by 0-cells, and every 0-cell can find at…
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…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
This work proposes a hierarchical clustering algorithm for high-dimensional datasets using the cyclic space of reversible finite cellular automata. In cellular automaton (CA) based clustering, if two objects belong to the same cycle, they…
In this paper, we construct a strongly universal cellular automaton on the line with 11 states and the standard neighbourhood. We embed this construction into several tilings of the hyperbolic plane and of the hyperbolic 3D space giving…
We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one…
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…
We present a simple one-dimensional Cellular Automaton (CA) which has the property that an initial state composed of two binary numbers evolves quickly into a final state which is their sum. We call this CA the Adding Cellular Automaton…
We study transformations of 2-, 4- and 6-bit numbers in interactions between traveling and stationary localizations in the Spiral Rule reaction-diffusion cellular automaton. The Spiral Rule automaton is a hexagonal ternary-state…
In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$.…
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state.…
While one-dimensional cellular automata have been well studied, there are relatively few results about multidimensional cellular automata; the investigation of cellular automata defined on Cayley trees constitutes an intermediate class.…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
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…
Thermal noise in a cellular automaton refers to a random perturbation to its function which eventually leads this automaton to an equilibrium state controlled by a temperature parameter. We study the 1-dimensional majority-3 cellular…