scholarly journals On the analysis of ''simple'' 2D stochastic cellular automata

2010 ◽  
Vol Vol. 12 no. 2 ◽  
Author(s):  
Damien Regnault ◽  
Nicolas Schabanel ◽  
Eric Thierry
Keyword(s):  
Cellular Automata ◽  
Time Step ◽  
Energy Functions ◽  
Stochastic Cellular Automata ◽  
Von Neumann ◽  
Rich Variety ◽  
Moore Neighborhood ◽  
International Audience ◽  
Definition Of ◽  
New Phenomena

International audience Cellular automata are usually associated with synchronous deterministic dynamics, and their asynchronous or stochastic versions have been far less studied although significant for modeling purposes. This paper analyzes the dynamics of a two-dimensional cellular automaton, 2D Minority, for the Moore neighborhood (eight closest neighbors of each cell) under fully asynchronous dynamics (where one single random cell updates at each time step). 2D Minority may appear as a simple rule, but It is known from the experience of Ising models and Hopfield nets that 2D models with negative feedback are hard to study. This automaton actually presents a rich variety of behaviors, even more complex that what has been observed and analyzed in a previous work on 2D Minority for the von Neumann neighborhood (four neighbors to each cell) (2007) This paper confirms the relevance of the later approach (definition of energy functions and identification of competing regions) Switching to the Moot e neighborhood however strongly complicates the description of intermediate configurations. New phenomena appear (particles, wider range of stable configurations) Nevertheless our methods allow to analyze different stages of the dynamics It suggests that predicting the behavior of this automaton although difficult is possible, opening the way to the analysis of the whole class of totalistic automata

scholarly journals Asynchronous Cellular Automata and Brownian Motion

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Philippe Chassaing ◽  
Lucas Gerin
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Cellular Automata ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Time Step ◽  
Interacting Particle ◽  
Asynchronous Cellular Automata ◽  
International Audience ◽  
A Cell

International audience This paper deals with some very simple interacting particle systems, \emphelementary cellular automata, in the fully asynchronous dynamics: at each time step, a cell is randomly picked, and updated. When the initial configuration is simple, we describe the asymptotic behavior of the random walks performed by the borders of the black/white regions. Following a classification introduced by Fatès \emphet al., we show that four kinds of asymptotic behavior arise, two of them being related to Brownian motion.

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.

Fundamental of Cellular Automata Theory

2017 ◽  
pp. 26-51
Keyword(s):  
Cellular Automata ◽  
Automata Theory ◽  
Linear Feedback ◽  
Random Number Generators ◽  
Von Neumann ◽  
One Dimensional ◽  
Asynchronous Cellular Automata ◽  
Local Functions ◽  
Definition Of

In this chapter, the author reviews the main historical aspects of the development of cellular automata. The basic structures of cellular automata are described. The classification of cellular automata is considered. A definition of a one-dimensional cellular automaton is given and the basic rules for one-dimensional cellular automata are described that allow the implementation of pseudo-random number generators. One-dimensional cellular automata with shift registers with linear feedback are compared. Synchronous two-dimensional cellular automata are considered, as well as their behavior for various using local functions. An analysis of the functioning of synchronous cellular automata for the neighborhoods of von Neumann and Moore is carried out. A lot of attention is paid to asynchronous cellular automata. The necessary definitions and rules for the behavior of asynchronous cellular automata are given.

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.

scholarly journals Surjective cellular automata far from the Garden of Eden

2013 ◽  
Vol Vol. 15 no. 3 (Automata, Logic and Semantics) ◽  
Author(s):  
Silvio Capobianco ◽  
Pierre Guillon ◽  
Jarkko Kari
Keyword(s):  
Cellular Automata ◽  
Automata Theory ◽  
Garden Of Eden ◽  
Amenable Groups ◽  
Von Neumann ◽  
International Audience

Automata, Logic and Semantics International audience One of the first and most famous results of cellular automata theory, Moore's Garden-of-Eden theorem has been proven to hold if and only if the underlying group possesses the measure-theoretic properties suggested by von Neumann to be the obstacle to the Banach-Tarski paradox. We show that several other results from the literature, already known to characterize surjective cellular automata in dimension d, hold precisely when the Garden-of-Eden theorem does. We focus in particular on the balancedness theorem, which has been proven by Bartholdi to fail on amenable groups, and we measure the amount of such failure.

scholarly journals Faster Methods for Identifying Nontrivial Energy Conservation Functions for Cellular Automata

2010 ◽  
Vol DMTCS Proceedings vol. AL,... (Proceedings) ◽  
Author(s):  
Leemon Baird ◽  
Barry Fagin
Keyword(s):  
Cellular Automata ◽  
General Theory ◽  
Energy Conservation ◽  
Linear Algebra ◽  
Solution Space ◽  
Basis Set ◽  
Complete List ◽  
Energy Functions ◽  
Game Of Life ◽  
International Audience

International audience The biggest obstacle to the efficient discovery of conserved energy functions for cellular auotmata is the elimination of the trivial functions from the solution space. Once this is accomplished, the identification of nontrivial conserved functions can be accomplished computationally through appropriate linear algebra. As a means to this end, we introduce a general theory of trivial conserved functions. We consider the existence of nontrivial additive conserved energy functions ("nontrivials") for cellular automata in any number of dimensions, with any size of neighborhood, and with any number of cell states. We give the first known basis set for all trivial conserved functions in the general case, and use this to derive a number of optimizations for reducing time and memory for the discovery of nontrivials. We report that the Game of Life has no nontrivials with energy windows of size 13 or smaller. Other $2D$ automata, however, do have nontrivials. We give the complete list of those functions for binary outer-totalistic automata with energy windows of size 9 or smaller, and discuss patterns we have observed.

Influence of Clearances and Thermal Effects on the Dynamic Behavior of Gear-Hydrodynamic Journal Bearing Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
R. Fargère ◽  
P. Velex
Keyword(s):  
Degrees Of Freedom ◽  
Integration Scheme ◽  
Time Step ◽  
Specific Element ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Gear Teeth ◽  
Proposed Model ◽  
Elastic Couplings ◽  
Definition Of

A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts, and hydrodynamic journal bearings. A specific element for wide-faced gears with nonlinear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements, whereas the bearing contributions are introduced based on the direct solution of Reynolds' equation. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time step integration scheme, a Newton–Raphson method, and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. A series of comparisons with the experimental results obtained on a test rig are given which prove that the proposed model is sound. Finally, a number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings, the clearance/elastic couplings interactions, etc. can be influential on static and dynamic tooth loading.

scholarly journals Three-state von Neumann cellular automata and pattern generation

2015 ◽  
Vol 39 (7) ◽  
pp. 2003-2024 ◽  
Author(s):  
Ugur Sahin ◽  
Selman Uguz ◽  
Hasan Akın ◽  
Irfan Siap
Keyword(s):  
Cellular Automata ◽  
Pattern Generation ◽  
Von Neumann
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