Related papers: Universal Cellular Automata and Class 4
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
A framework for implementing reservoir computing (RC) and extreme learning machines (ELMs), two types of artificial neural networks, based on 1D elementary Cellular Automata (CA) is presented, in which two separate CA rules explicitly…
Wolfram [2, p. 707] and Cook [1, p. 3] claim to prove that a (2,5) Turing machine (2 states, 5 symbols) is universal, via a universal cellular automaton known as Rule 110. The first part of this paper points out a critical gap in their…
Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in…
A brief introduction to Wolfram's work on cellular automata.
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…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
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…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
We investigate critical properties of a class of number-conserving cellular automata (CA) which can be interpreted as deterministic models of traffic flow with anticipatory driving. These rules are among the only known CA rules for which…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the…
It is speculated that there is a relationship between 1/f noise and computational universality in cellular automata. We use genetic algorithms to search for one-dimensional and two-state, five-neighbor cellular automata which have 1/f-type…
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We…
We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…
Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…
One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular…
Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular…
Cellular automata are computers, similar to Turing machines. The main difference is that Turing machines use a one-dimensional tape, whereas cellular automata use a two-dimensional grid. The best-known cellular automaton is the Game of…
This article presents a new characterization of controllability and regional controllability of Deterministic Cellular Automata (CA for short). It focuses on analyzing these problems within the framework of control theory, which have been…