Related papers: A new universal cellular automaton on the ternary …

We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the…

We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding…

We present herein an introduction to implementing 2-color cellular automata on quantum annealing systems, such as the D-Wave quantum computer. We show that implementing nearest-neighbor cellular automata is possible. We present an…

Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…

We prove that the (language of the) asymptotic set (and the nonwandering set) of a one-dimensional cellular automaton can be $\SIGMA^1_1$-hard. We do not go into much detail, since the constructions are relatively standard.

We present a preliminary study of a new class of two-input cellular automata called eventually number-conserving cellular automata characterized by the property of evolving after a finite number of time steps to states whose number of…

A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…

This paper introduces a hierarchical cellular automaton (HCA)model for simulation of distributed self-organizing control of traffic signals at intersections in road network. The proposed HCA consists of three hierarchy levels that describe…

We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…

Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…

We present ongoing work on a tool that consists of two parts: (i) A raw micro-level abstract world simulator with an interface to (ii) a 3D game engine, translator of raw abstract simulator data to photorealistic graphics. Part (i)…

We consider the group structure of quantum cellular automata (QCA) modulo circuits and show that it is abelian even without assuming the presence of ancillas, at least for most reasonable choices of control space; this is a corollary of a…

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The problem…

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 this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, (see Margenstern, 2000, 2007 and Margenstern, Morita, 2001) and we consider the global function defined on all possible configurations.…

This paper presents an application of the Infinite Unit Axiom, introduced by Yaroslav Sergeyev, (see [11] - [14]) to the development of one-dimensional cellular automata. This application allows the establishment of a new and more precise…

The positive rates conjecture states that a one-dimensional probabilistic cellular automaton (PCA) with strictly positive transition rates must be ergodic. The conjecture has been refuted by G\'acs, whose counterexample is a cellular…

Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under…

We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore…

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…