Cellular Automata with Repetitive Initial Conditions

2007 ◽  
Keyword(s):  
Cellular Automata ◽  
Initial Conditions

Computational Foundations of the Anticipatory Artificial Autopoietic Cellular Automata

2021 ◽  
pp. 289-307
Author(s):  
Daniel M. Dubois ◽  
Stig C. Holmberg
Keyword(s):  
Artificial Intelligence ◽  
Cellular Automata ◽  
Living Cell ◽  
Artificial Life ◽  
Initial Conditions ◽  
Living Cells ◽  
Asymmetric Membrane

A survey of the Varela automata of autopoiesis is presented. The computation of the Varela program, with initial conditions given by a living cell, is not able to self-maintain the membrane of the living cell. In this chapter, the concept of anticipatory artificial autopoiesis (AAA) is introduced. In this chapter, the authors present a new algorithm of the anticipatory artificial autopoiesis, which extend the Varela automata. The main enhancement consists in defining an asymmetric membrane of the artificial lining cell. The simulations show the anticipatory generation of artificial living cells starting with any initial conditions. The new concept of anticipatory artificial autopoiesis is related to artificial life (Alife) and artificial intelligence (AI). This is a breakthrough in the computational foundation of autopoiesis.

Languages, equicontinuity and attractors in cellular automata

1997 ◽  
Vol 17 (2) ◽  
pp. 417-433 ◽  
Author(s):  
PETR KŮRKA
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
State Space ◽  
Finite Type ◽  
Measure Zero ◽  
Initial Conditions ◽  
The State ◽  
Subshift Of Finite Type ◽  
Topologically Transitive ◽  
The Third

We consider three related classifications of cellular automata: the first is based on the complexity of languages generated by clopen partitions of the state space, i.e. on the complexity of the factor subshifts; the second is based on the concept of equicontinuity and it is a modification of the classification introduced by Gilman [9]. The third one is based on the concept of attractors and it refines the classification introduced by Hurley [16]. We show relations between these classifications and give examples of cellular automata in the intersection classes. In particular, we show that every positively expansive cellular automaton is conjugate to a one-sided subshift of finite type and that every topologically transitive cellular automaton is sensitive to initial conditions. We also construct a cellular automaton with minimal quasi-attractor, whose basin has measure zero, answering a question raised in Hurley [16].

scholarly journals Traffic Flow Modeling on Road Networks Using Cellular Automata Theory

2018 ◽  
Vol 7 (2.28) ◽  
pp. 225 ◽  
Author(s):  
A Chechina ◽  
N Churbanova ◽  
M Trapeznikova ◽  
A Ermakov ◽  
M German
Keyword(s):  
Cellular Automata ◽  
Initial Conditions ◽  
Road Networks ◽  
Original Model ◽  
Program Package ◽  
Automata Theory ◽  
Flow Modeling ◽  
Traffic Flows ◽  
Urban Road ◽  
The Road

The paper deals with mathematical modeling of traffic flows on urban road networks. The original model is based on the cellular automata theory and presents a generalization of Nagel-Schreckenberg model to a multilane case.Numerical realization of the model is represented in a form of the program package that consists of two modules: User Interface and Visualization module (for setting initial conditions and modelling parameters and visual representation of calculations) and Computation module (for calculations).Computations are carried out for each element of the road (i.e. T or X type intersection, straight road fragment) separately and in parallel, that allows performing calculations on various complex road networks. Different kinds of average characteristics (e.g. the capacity of the crossroad) can be also obtained using the program package. 

Emergent Structures

2010 ◽  
pp. 83-113
Author(s):  
Eleonora Bilotta ◽  
Pietro Pantano
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Initial Conditions ◽  
Natural Sciences ◽  
Forward Problem ◽  
Second Step ◽  
Large Collection ◽  
Parameter Values

There are two classes of problem in the study of Cellular Automata. The forward. problem is the problem of determining the properties of the system. Solutions often consist of finding quantities that are computable on a rules table and characterizing the behavior of the rule upon repeated iterations, starting from different initial conditions. Solutions to the backwards problem begin with the properties of a system and find a rule or a set of rules which have these properties. This is especially useful in the application of Cellular Automata to the natural sciences, when researchers deal with a large collection of phenomena (Gutowitz, 1989). Another approach is to identify the basic structures of a Cellular Automaton (Adamatzky, 1995). Once these are known it becomes possible to develop specific models for particular systems and to detect general principles applicable to a wide variety of systems (Wolfram, 1984; Lam, 1998). According to Adamatzky, the identification of a system consists of two related steps, namely specification and estimation. In specification we choose a useful and efficient description of the system: perhaps an equation and a set of parameters. The second step involves the estimation of parameter values for the equation: exploiting measures of similarity.

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.

scholarly journals ASYMPTOTIC BEHAVIOR AND RATIOS OF COMPLEXITY IN CELLULAR AUTOMATA

2013 ◽  
Vol 23 (09) ◽  
pp. 1350159 ◽  
Author(s):  
HECTOR ZENIL ◽  
ELENA VILLARREAL-ZAPATA
Keyword(s):  
Asymptotic Behavior ◽  
Cellular Automata ◽  
Kolmogorov Complexity ◽  
Initial Conditions ◽  
Limit Function ◽  
Computing Systems ◽  
Symbolic Computing ◽  
Rule Space ◽  
Simple Rules ◽  
Block Entropy

We study the asymptotic behavior of symbolic computing systems, notably one-dimensional cellular automata (CA), in order to ascertain whether and at what rate the number of complex versus simple rules dominate the rule space for increasing neighborhood range and number of symbols (or colors), and how different behavior is distributed in the spaces of different cellular automata formalisms. Using two different measures, Shannon's block entropy and Kolmogorov complexity, the latter approximated by two different methods (lossless compressibility and block decomposition), we arrive at the same trend of larger complex behavioral fractions. We also advance a notion of asymptotic and limit behavior for individual rules, both over initial conditions and runtimes, and we provide a formalization of Wolfram's classification as a limit function in terms of Kolmogorov complexity.

scholarly journals Dynamic Partial Encryption System for Digital Image

2019 ◽  
pp. 10-16
Author(s):  
Gustavo Rodríguez- Cardona ◽  
Leonardo Humberto Ramírez- Beltrán ◽  
Marco Tulio Ramírez- Torres
Keyword(s):  
Cellular Automata ◽  
Digital Image ◽  
Initial Conditions ◽  
Security Analysis ◽  
Data Encryption ◽  
Encryption Algorithm ◽  
Secret Key ◽  
Partial Encryption ◽  
Attractive Option ◽  
Bit Planes

The present investigation is proposing a new partial encryption algorithm for digital image, using the synchronization of cellular automata based on the local rule 90. Unlike other partial encryption algorithm, which become vulnerable to attacks such as Replacement Attack or Reconstruction Attack, this system encodes different bit planes, in function of the secret key, that is, for each block of clear text, different bits are encrypted to prevent that with an elimination operation of the encrypted bits information can be revealed. The synchronization of cellular automata has proven to be a useful tool for data encryption because it is sensitivity to initial conditions and, in addition, rule 90 is considered a chaotic standard. Both characteristics ensure cryptographic and perceptive security. Based on the results of the security analysis, this research could be an attractive option for image encryption with less computer cost and without compromising information confidentiality.

scholarly journals Evolving Interesting Initial Conditions for Cellular Automata of the Game of Life Type

2012 ◽  
Vol 21 (1) ◽  
pp. 57-70 ◽  
Author(s):  
Manuel Alfonseca ◽  
◽  
Francisco José Soler Gil ◽  
Keyword(s):  
Cellular Automata ◽  
Initial Conditions ◽  
Game Of Life ◽  
Life Type

scholarly journals Power law behavior of Elementary Cellular Automata

2021 ◽  
Author(s):  
Jorge Laval
Keyword(s):  
Cellular Automata ◽  
Power Law ◽  
Initial Conditions ◽  
Percolation Clusters ◽  
Elementary Cellular Automata ◽  
Random Initial Conditions

This paper shows that the percolation clusters from elementary cellular automata {30, 45, 60, 86, 99, 105, 129, 150, 153, 169, 182, 183, 184, 195 and 225 exhibit strong power law behavior, either under random initial conditions, a single occupied cell, or both. Most of the tail exponents are less than unity, implying diverging means and variances of cluster sizes. The analysis presented here is admittedly coarse in an effort to expedite its dissemination.

Sign in / Sign up

Export Citation Format

Share Document