Related papers: The GraftalLace Cellular Automaton
Several cellular automata (CA) models have been developed to simulate self-organization of multiple levels of structures. However, they do not obey microscopic reversibility and conservation laws. In this paper, we describe the construction…
Parallel algorithms for solving any image processing task is a highly demanded approach in the modern world. Cellular Automata (CA) are the most common and simple models of parallel computation. So, CA has been successfully used in the…
In this paper we consider invertible one-dimensional linear cellular automata (CA hereafter) defined on a finite alphabet of cardinality $p^k$, i.e. the maps $T_{f[l,r]}:\mathbb{Z}^{\mathbb{Z}}_{p^k}\to\mathbb{Z}^{\mathbb{Z}}_{p^k}$ which…
This study introduces EngramNCA, a neural cellular automaton (NCA) that integrates both publicly visible states and private, cell-internal memory channels, drawing inspiration from emerging biological evidence suggesting that memory storage…
A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…
In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal…
Quantum-dot Cellular Automata (QCA) may offer a viable alternative of traditional transistor-based technology at the nanoscale. When modeling a QCA circuit, the number of degrees of freedom necessary to describe the quantum mechanical state…
We present a method to eliminate redundancy in the transition tables of Boolean automata: schema redescription with two symbols. One symbol is used to capture redundancy of individual input variables, and another to capture permutability in…
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…
Memristors are novel non volatile devices that manage to combine storing and processing capabilities in the same physical place.Their nanoscale dimensions and low power consumption enable the further design of various nanoelectronic…
Larger than Life cellular automaton (LtL) is a class of cellular automata and is a generalization of the game of Life by extending its neighborhood radius. We have studied the three-dimensional extension of LtL. In this paper, we show a…
Reversibility of a one-dimensional finite cellular automaton (CA) is dependent on lattice size. A finite CA can be reversible for a set of lattice sizes. On the other hand, reversibility of an infinite CA, which is decided by exploring the…
Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
Over an arbitrary commutative ring $R$, we develop a theory of quantum cellular automata. We then use algebraic K-theory to construct a space $\mathbf{Q}(X)$ of quantum cellular automata (QCA) on a given metric space $X$. In most cases of…
Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the…
In this article, I propose a systematic method for the inverse ultra-discretization of cell automata using a functionally complete operation. We derive difference equations for the 256 kinds of elementary cellular automata(ECA) introduced…
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 collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations).…