Universal Computation in a Simplified Brownian Cellular Automaton with von Neumann Neighborhood

2019 ◽  
Vol 165 (2) ◽  
pp. 139-156 ◽  
Author(s):  
Wen-Li Xu ◽  
Jia Lee ◽  
Hui-Hui Chen ◽  
Teijiro Isokawa
Keyword(s):  
Cellular Automaton ◽  
Von Neumann ◽  
Universal Computation

Lifelike Self-Replicators

2010 ◽  
pp. 210-247
Author(s):  
Eleonora Bilotta ◽  
Pietro Pantano
Keyword(s):  
Cellular Automaton ◽  
Turing Machine ◽  
Digital Computer ◽  
Initial Conditions ◽  
Von Neumann ◽  
One Dimensional ◽  
Game Of Life ◽  
Universal Computation

The concept of a cellular automaton derives from John von Neumann’s studies of the logic of life. In these studies, von Neumann focused on self-replicating structures with universal computational capabilities. Given the appropriate initial conditions, a universal computer can perform any finite computation, reproducing even the most complex biological behaviors. It is well known that the ECAs described in (Wolfram, 2002) and the Game of Life (Gardner, 1970; Evans, 2003; Adachi et al., 2008) have universal computational capabilities. It has been shown, furthermore, that certain one-dimensional CAs can generate structures that are equivalent to the components of an idealized digital computer, and that, by connecting these components in different ways, it is possible to implement any kind of algorithm. In brief, these CAs are equivalent to the better known - and simpler - Turing machine and share its ability to perform universal computation (Smith 1971).

Models and Paradigms of Cellular Automata With a Variable Set of Active Cells

2021 ◽  
pp. 75-98
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Variable Number ◽  
Point Of View ◽  
Modes Of Operation ◽  
Von Neumann ◽  
Asynchronous Cellular Automata ◽  
Cad Models

The chapter describes the functioning model of an asynchronous cellular automaton with a variable number of active cells. The rules for the formation of active cells with new active states are considered. Codes of active states for the von Neumann neighborhood are presented, and a technique for coding active states for other forms of neighborhoods is described. Several modes of operation of asynchronous cellular automata from the point of view of the influence of active cells are considered. The mode of coincidence of active cells and the mode of influence of neighboring active cells are considered, and the mode of influence of active cells of the surroundings is briefly considered. Algorithms of cell operation for all modes of the cellular automata are presented. Functional structures of cells and their CAD models are constructed.

scholarly journals The resolution of a mathematically bad-defined problem in the approximation of a cellular automation by the example of the description of human states

2021 ◽  
Vol 2056 (1) ◽  
pp. 012062
Author(s):  
E V Kalashnikov ◽  
A A Sheryomukhina ◽  
V D Filatov
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Cellular Automaton ◽  
Finite Differences ◽  
Mutual Influence ◽  
Rate Of Change ◽  
System Of Differential Equations ◽  
Von Neumann ◽  
Sequential Execution ◽  
Cellular Automation

Abstract A mathematical model describing the mutual influence of bad-defined various human characteristics is constructed. This model is described by a system of differential equations that reflect the “rate” of change in a characteristic as a function of the frequency of interaction with other characteristics. The transition from differential equations to equations in finite differences and the introduction of the von Neumann neighborhood on the resulting square space of the frequency of interaction of various human characteristics allows us to introduce a cellular automaton. The sequential execution of iterations in the cellular automaton allows to track how each of the entered characteristics depends on the behavior of other characteristics.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata

2017 ◽  
pp. 66-108
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Random Number ◽  
Random Number Generator ◽  
Active Cell ◽  
Time Step ◽  
Random Number Generators ◽  
Von Neumann ◽  
Asynchronous Cellular Automata ◽  
Pseudo Random Number

The fourth chapter deals with the use of asynchronous cellular automata for constructing high-quality pseudo-random number generators. A model of such a generator is proposed. Asynchronous cellular automata are constructed using the neighborhood of von Neumann and Moore. Each cell of such an asynchronous cellular state can be in two states (information and active states). There is only one active cell at each time step in an asynchronous cellular automaton. The cell performs local functions only when it is active. At each time step, the active cell transmits its active state to one of the neighborhood cells. An algorithm for the operation of a pseudo-random number generator based on an asynchronous cellular automaton is described, as well as an algorithm for working a cell. The hardware implementation of such a generator is proposed. Several variants of cell construction are considered.

Cellular Automaton Modeling of Dynamic Recrystallisation Microstructure Evolution for 316LN Stainless Steel

2016 ◽  
Vol 693 ◽  
pp. 548-553 ◽  
Author(s):  
Hai Peng Ji ◽  
Li Ge Zhang ◽  
Jing Liu ◽  
Tai Yong Wang
Keyword(s):  
Dynamic Recrystallization ◽  
Cellular Automaton ◽  
Grain Growth ◽  
Volume Fraction ◽  
Von Neumann ◽  
Modeling Methodology ◽  
Average Grain Size ◽  
Dynamic Recrystallisation ◽  
Ca Model ◽  
Kinetic Transformation

Based on the theoretical model and physical mechanism of dynamic recrystallization (DRX) in metal materials, the dislocation density change, nucleation and grain growth model during the process of DRX are taken into account. And according to the nucleation driven by dislocation and grain growth kinetic, transformation rules are made. A modeling methodology coupling fundamental metallurgical principles based on amended nucleation rate with the cellular automaton (CA) technique is here derived to simulate the 316LN.The two-dimensional CA model uses quadrilateral element and periodic boundary condition and Von-Neumann neighbor type. The influence of strain, strain rate and deformation temperature on dynamic recrystallization volume fraction and average grain size are analyzed on the basis of established CA model.

scholarly journals EVOLUTION OF TWO-DIMENSIONAL CELLULAR AUTOMATA. NEW FORMS OF PRESENTATION

2021 ◽  
Vol 3 (1) ◽  
pp. 85-90
Author(s):  
S. M. Bilan ◽  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Color Image ◽  
The State ◽  
Dynamic Processes ◽  
State Change ◽  
Two Dimensional ◽  
Time Step ◽  
Von Neumann ◽  
Elementary Cellular Automata

The paper considers cellular automata and forms of reflection of their evolution. Forms of evolution of elementary cellular automata are known and widely used, which allowed specialists to model different dynamic processes and behavior of systems in different directions. In the context of the easy construction of the form of evolution of elementary cellular automata, difficulties arise in representing the form of evolution of two-dimensional cellular automata, both synchronous and asynchronous. The evolution of two-dimensional cellular automata is represented by a set of states of two-dimensional forms of cellular automata, which complicates the perception and determination of the dynamics of state change. The aim of this work is to solve the problem of a fixed mapping of the evolution of a two-dimensional cellular automaton in the form of a three-dimensional representation, which is displayed in different colors on a two-dimensional image The paper proposes the evolution of two-dimensional cellular automata in the form of arrays of binary codes for each cell of the field. Each time step of the state change is determined by the state of the logical "1" or "0". Moreover, each subsequent state is determined by increasing the binary digit by one. The resulting binary code identifies the color code that is assigned to the corresponding cell at each step of the evolution iteration. As a result of such coding, a two-dimensional color matrix (color image) is formed, which in its color structure indicates the evolution of a two-dimensional cellular automaton. To represent evolution, Wolfram coding was used, which increases the number of rules for a two-dimensional cellular automaton. The rules were used for the von Neumann neighborhood without taking into account the own state of the analyzed cell. In accordance with the obtained two-dimensional array of codes, a discrete color image is formed. The color of each pixel of such an image is encoded by the obtained evolution code of the corresponding cell of the two-dimensional cellular automaton with the same coordinates. The bitness of the code depends on the number of time steps of evolution. The proposed approach allows us to trace the behavior of the cellular automaton in time depending on its initial states. Experimental analysis of various rules for the von Neumann neighborhood made it possible to determine various rules that allow the shift of an image in different directions, as well as various affine transformations over images. Using this approach, it is possible to describe various dynamic processes and natural phenomena.

An Implementation of von Neumann's Self-Reproducing Machine

1995 ◽  
Vol 2 (4) ◽  
pp. 337-354 ◽  
Author(s):  
Umberto Pesavento
Keyword(s):  
Cellular Automaton ◽  
State Transition ◽  
The State ◽  
Transition Rule ◽  
John Von Neumann ◽  
Von Neumann ◽  
Special Case

This article describes in detail an implementation of John von Neumann's self-reproducing machine. Self-reproduction is achieved as a special case of construction by a universal constructor. The theoretical proof of the existence of such machines was given by John von Neumann in the early 1950s [6], but was first implemented in 1994, by the author in collaboration with R. Nobili. Our implementation relies on an extension of the state-transition rule of von Neumann's original cellular automaton. This extension was introduced to simplify the design of the constructor. The main operations in our constructor can be mapped into operations of von Neumann's machine.

Reliable Self-Replicating Machines in Asynchronous Cellular Automata

2007 ◽  
Vol 13 (4) ◽  
pp. 397-413 ◽  
Author(s):  
Jia Lee ◽  
Susumu Adachi ◽  
Ferdinand Peper
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Essential Property ◽  
Two Dimensional ◽  
Von Neumann ◽  
Asynchronous Cellular Automata ◽  
Self Replication

We propose a self-replicating machine that is embedded in a two-dimensional asynchronous cellular automaton with von Neumann neighborhood. The machine dynamically encodes its shape into description signals, and despite the randomness of cell updating, it is able to successfully construct copies of itself according to the description signals. Self-replication on asynchronously updated cellular automata may find application in nanocomputers, where reconfigurability is an essential property, since it allows avoidance of defective parts and simplifies programming of such computers.

Lectures on von Neumann Algebras

2019 ◽  
Author(s):  
Serban-Valentin Stratila ◽  
Laszlo Zsido
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann
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