Critical points of two-dimensional bootstrap percolation-like cellular automata

1990 ◽  
Vol 58 (5-6) ◽  
pp. 1239-1244 ◽  
Author(s):  
Roberto H. Schonmann
Keyword(s):  
Cellular Automata ◽  
Critical Points ◽  
Bootstrap Percolation ◽  
Two Dimensional

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

Two-dimensional critical points and critical isotherms

1985 ◽  
Vol 32 (7) ◽  
pp. 4760-4762 ◽  
Author(s):  
Jeffrey J. Hamilton
Keyword(s):  
Critical Points ◽  
Two Dimensional

Equilibrium and nonequilibrium models on solomon networks with two square lattices

2017 ◽  
Vol 28 (08) ◽  
pp. 1750099
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Critical Points ◽  
Majority Vote ◽  
Universality Class ◽  
2D Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

scholarly journals Design of a Hybrid Programmable 2-D Cellular Automata Based Pseudo Random Number Generator

2020 ◽  
Vol 8 (6) ◽  
pp. 5741-5748
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Hamming Distance ◽  
Random Number Generator ◽  
Number Generator ◽  
Two Dimensional ◽  
Pseudo Random Number ◽  
Rule Set ◽  
Initial Seed ◽  
Pseudo Random Number Generator

This paper proposes a hybrid programmable two-dimensional Cellular Automata (CA) based pseudo-random number generator which includes a newly designed rule set. The properties and evolution of one and two dimensional CA are revisited. The various metrics for evaluating CA as a Pseudo-Random Number Generator (PRNG) are discussed. It is proved that the randomness is high irrespective of the initial seed by applying this newly designed rule set. The PRNG is tested against a popular statistical test called Diehard test suite and the results show that the PRNG is highly random. The chaotic measures like entropy, hamming distance and cycle length have been measured

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