The Effects of Boundary Conditions on Cellular Automata

2019 ◽  
Vol 28 (1) ◽  
pp. 97-124
Author(s):  
Brian J. LuValle ◽  
Keyword(s):  
Cellular Automata ◽  
Boundary Conditions

Recurrent Misconceptions in the Study of CA Reversibility on Triangular Grids

2021 ◽  
Vol 31 (01) ◽  
pp. 2150014
Author(s):  
Barbara Wolnik ◽  
Maciej Dziemiańczuk ◽  
Bernard De Baets
Keyword(s):  
Cellular Automata ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Triangular Grids

We present counterexamples illustrating that the characterization of the reversibility of linear cellular automata on finite triangular grids given by Uguz et al. [2017] and Uguz et al. [2019] is not valid, neither in the case of null boundary conditions nor in the case of periodic boundary conditions.

scholarly journals A comparative study of 2d Ising model at different boundary conditions using Cellular Automata

2018 ◽  
Vol 29 (08) ◽  
pp. 1850066
Author(s):  
Jahangir Mohammed ◽  
Swapna Mahapatra
Keyword(s):  
Ising Model ◽  
Cellular Automata ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Spontaneous Magnetization ◽  
Spin Systems ◽  
Square Lattice ◽  
Random Orientation ◽  
Lattice Size ◽  
Different Types

Using Cellular Automata, we simulate spin systems corresponding to [Formula: see text] Ising model with various kinds of boundary conditions (bcs). The appearance of spontaneous magnetization in the absence of magnetic field is studied with a [Formula: see text] square lattice with five different bcs, i.e. periodic, adiabatic, reflexive, fixed ([Formula: see text] or [Formula: see text]) bcs with three initial conditions (all spins up, all spins down and random orientation of spins). In the context of [Formula: see text] Ising model, we have calculated the magnetization, energy, specific heat, susceptibility and entropy with each of the bcs and observed that the phase transition occurs around [Formula: see text] as obtained by Onsager. We compare the behavior of magnetization versus temperature for different types of bcs by calculating the number of points close to the line of zero magnetization after [Formula: see text] at various lattice sizes. We observe that the periodic, adiabatic and reflexive bcs give closer approximation to the value of [Formula: see text] than fixed [Formula: see text] and fixed [Formula: see text] bcs with all three initial conditions for lattice sizes less than [Formula: see text]. However, for lattice size between [Formula: see text] and [Formula: see text], fixed [Formula: see text] bc and fixed [Formula: see text] bc give closer approximation to the [Formula: see text] with initial conditions all spin down configuration and all spin up configuration, respectively.

Transient and cyclic behavior of cellular automata with null boundary conditions

1993 ◽  
Vol 73 (1-2) ◽  
pp. 159-174 ◽  
Author(s):  
John G. Stevens ◽  
Ronald E. Rosensweig ◽  
A. E. Cerkanowicz
Keyword(s):  
Cellular Automata ◽  
Boundary Conditions ◽  
Cyclic Behavior

ON THE REVERSIBILITY OF 150 WOLFRAM CELLULAR AUTOMATA

2006 ◽  
Vol 17 (07) ◽  
pp. 975-983 ◽  
Author(s):  
A. MARTÍN DEL REY ◽  
G. RODRÍGUEZ SÁNCHEZ
Keyword(s):  
Cellular Automata ◽  
Boundary Conditions ◽  
Cellular Automaton ◽  
Number Of Cells

In this paper, the reversibility problem for 150 Wolfram cellular automata is tackled for null boundary conditions. It is explicitly shown that the reversibility depends on the number of cells of the cellular automaton. The inverse cellular automaton for each case is also computed.

Reversible elementary cellular automaton with rule number 150 and periodic boundary conditions over 𝔽p

2015 ◽  
Vol 26 (11) ◽  
pp. 1550120 ◽  
Author(s):  
A. Martín del Rey ◽  
G. Rodríguez Sánchez
Keyword(s):  
Cellular Automata ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Discrete Dynamical Systems ◽  
Circulant Matrices ◽  
Cellular Space ◽  
Finite State ◽  
Rule Number ◽  
Elementary Cellular Automaton

The study of the reversibility of elementary cellular automata with rule number 150 over the finite state set 𝔽p and endowed with periodic boundary conditions is done. The dynamic of such discrete dynamical systems is characterized by means of characteristic circulant matrices, and their analysis allows us to state that the reversibility depends on the number of cells of the cellular space and to explicitly compute the corresponding inverse cellular automata.

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